One thing I'd recommend is having the credit to Andrew Medeiros (as a side note the name is misspelled as Meideros) in its own section at the end or start, instead of in the middle underneath a header. Same goes for the Gig rules and other things you've taken inspiration/borrowed. One additional thing that is nice to see in many "mini-hacks" of PbtA that don't have comprehensive rules of their own is where the piecemeal rules are taken from. There are rules for threats, advanced moves, highlighted moves, etc. It's nice to see where they are from if a reader wants to check them out for some more detail on how they work.
Also, if possible try to credit the artists whose artwork you're using. It's a nice gesture.
With those two out of the way, I have some questions, many purely about wording. This is going to be long, and probably will feel harsher than I intend it to be; I do this because I really like PbtA and I really like Star Wars. And I want to see good come out of the combination of the two.
Basic Moves
I've Got a Bad Feeling About This: The description for the move feels a bit wishy-washy. "When you want to make a move" feels meaningless to me, because the defining feature of making a move is actually doing what the move entails. While the stats and descriptions of the moves aren't bad, lumping them all into a single move that gets triggered "when you want to make a move" removes the above idea of actually doing a move. The move itself can stay (though I could also argue about separating them), but I'd rephrase it to something else. Also, I don't think the name of the move is the best. To me, that name evokes intuition and gut feelings rather than action.
Suffer Wounds: "When you take damage as established by the fiction"; you need to have some place where people can draw the rough damage numbers from. Some guidelines outside of the weapon damage listings. No doubt I feel that list exists somewhere, but make it explicit (and preferably refer to it in the description). The wording is also rather vague "can choose something" and "instead of some". It could do with some rephrasing and shortening. Perhaps into "On a 10+, the MC can reduce your harm taken by 1 to inflict one of the 7-9 conditions on you."
Suffer a Debility: Define debilities better. Right now it's just "a debility". The final sentence is a bit too long as well. "Debilities cannot be (missed a word there) removed easily, they can only be removed by installing cyberware." could just be shortened to "Debilities can only be removed by installing cyberware (or other intensive treatments)." Not a huge fan of reducing stats, since losing an arm is already a penalty, but that's just an opinion. Also you haven't mentioned who chooses the stat to be lowered.
Firing Solution: I'm unsure what the name of the move is referring to. I'd also probably have these rules not as a move, but as just part of a section about health and taking damage. As a move it just doesn't really do much.
Heal Up: "without the aid of a medical professional (like the Medic)" works better, because right now it implies that non-player doctors can't do much. An insane conclusion to draw, but better safe than sorry. Not a huge fan of the consequences, they make the Medic character feel like a necessity if the MC can just make your character not play for the next session or three at a whim. Having to use this move multiple times to heal your wounds makes it even worse. And the final consequence, "requiring constant monitoring and care from someone competent", feels a bit weird. Wouldn't that competent person be able to heal your wounds better as if they were a medic? That's what competent implies.
Take it easy: Not sure per-hour rates are the greatest for Star Wars. How often does the genre track time that way? I'd rather make it a fuzzy timespan. Also feels like it could be incorporated into the larger health/damage rules that I mentioned earlier.
Guns Blazing: Mention how much harm you suffer or inflict, especially with the options available. What "suffer little harm" means can vary from person to person (typically I've seen it as +/- 1 harm). As a minor note, if you're going to go with the "four (4)" option of having both there, be consistent.
Duck and Cover: I'd add this to the Guns Blazing move, instead of making it a move of its own. The two extra options are weird as well. One reduces the harm suffered by half, and the other... redirects half of the harm to your cover. What exactly is the difference there?
Stand in Defense: Seems okay, all in all, though again with the suffering/inflicting harm it's nice to know just how much you get.
Read a Person/Situation: Personally I prefer the two being separate moves. But aside from that, make sure that the people know they're meant to answer honestly. Maybe even have players mark XP for answering questions they don't want to as an incentive.
Trust Your Feelings: You have to define "new insight" a bit better. What does it mean? How is it conveyed to the player (ie, out-of-character)? What are the extents and how is this different from the questions in Read a Person/Situation move? I'd probably put another list of questions for this move, but focused around introspection instead of perception.
We're all fine here... How are you?: Long move name, I'd find something else. A bit of a wording fumble with "You can push past them and rush it,
but not quite clear" (emphasis for the fumble). "But you're not quite clear" is better. The miss is better phrased as something else than a movie reference. "They see through your lies immediately" works a lot better.
I Know a Guy... (Circles): The result is a bit poorly phrased. The 7-9 result should be "on a 7-9, as with 10+ but choose one". Also, the contact not being" as loyal as you hoped" and "you may get a light betrayal" seem redundant as options go. In addition, "you owe THEM a favor" implies that favors have been talked about, which isn't the case as favors are never mentioned. Possibly a remnant from an earlier build? Regardless, best to just remove the capitalization, and also make certain that the player does actually owe them a favor, instead of the NPC just seeing it that way.
Apply Leverage/Bribes: Combining these two because they feel relevant. I think Apply Leverage seems pretty standard to me, think I've seen that exact wording somewhere else. But Bribes seems entirely useless to me. Unless you're awful at Suave it's essentially using one money to get someone to want you to do something, which is something you'd likely get anyway by just rolling (58% chance of at least a 7 without any modifier). If you want to implement bribes, I'd rather have spending credits give a bonus to the Apply Leverage check instead of counting as an immediate 7, with rich people requiring more credits spent.
Put the Word Out: I'd like some example strings, but the MC should choose them. Right now it's a bit vague on just what kinds of strings there are. While it's not difficult to come up with some kinds of strings, it's nice to know some ways on how you can get screwed over. Always getting (potential) access to what you're looking for seems also slightly weird at times, but I don't mind it too much.
Hit the Duracrete: Oh god I hate these Star Wars material names. But anyway. This seems like an offshoot of Put the Word Out, since you're looking for something in both cases. Not sure why that needs credits and this one needs a skill check, as they're both kinda the same thing. I'd fold the two moves together for a rework.
Aid or Interfere: Pretty standard as far as I can tell. Nothing wrong with that. I'd mention stacking help as a thing that's not allowed.
Highlights and Experience: Not gonna lie, I don't like highlighting as a mechanic, especially in this way. There are very few ways to gain experience so far, and the primary source seems to be using as much of two stats as you can. I don't like that option, because it'll lead to very predictable results (players will probably default to picking a stat that is good) during play. Also it feels very weird to have these two semi-"moves" under the same paragraph.
Page 3 - assorted stuff
Races and droids: Races are fine, having no mechanical benefit by default is pretty okay in my books.
Droids: Got a bit of vague language again. What is a "repair kit" and what does that mean for the healing moves? Where are you drawing the "most nobles will not speak to a droid" part from? It seems a bit heavy handed, especially just after saying that stereotypes of races aren't true. Same with the designated owner thing. Making those imperatives feels just odd and restrictive.
Attempted Repair: Why are the rules for repairing things here instead of in the basic rules? You also contradict yourself with saying that only two playbooks can attempt repairs, then saying that everyone else gets -1. That is also design I do not like. Instead of pushing others down with penalties, push the others up with benefits. For the results "it may re-break in times of stress" and "it will cause issues later" are effectively the same thing.
Cyberware: Why can't you get a new cyberware if one is already damaged? If you can attach a robot arm to a character, you think you could detach the old and reattach a new one? What more, this does make it feel like characters are on a long-term downward spiral with their stats, and eventually everyone will be half-robot and then they'll just have bad stats the longer they play, unless they die first and replace their characters. While appropriate for some genres, Star Wars isn't that. These rules just don't seem like a fun prospect for me.
Alien Weirdness: You have another list of the races. So... Yeah, there's that for one. You have to work on this a lot more, to be honest. Right now, saying "create a move for a race" is just far too vague for many reasons.
Sex and Star Wars: While I'm all about informing players of the type of game they're getting into, this part seems way too heavy handed and seems more obsessed with the topic than is really necessary. Sex has never been a prominent part of Star Wars, and as such the very unsubtle example given is just completely out of place.
Overall for the basic moves, there's a lot of... Weirdness to it. Things don't feel like they form a cohesive whole just yet. The health rules feel all over the place, as well as other inconsistencies between moves interacting with each other. Rugged seems to have a vast majority of combat moves dedicated to it, which isn't necessarily the best idea.
Now, it should be noted that I haven't gone through the playbooks yet, so the interactions between playbooks and the basic moves might shift things around, but I can only write so much at once. With that in mind, I'm going to take a break. I may revisit the playbooks later, but you'll understand that going through all the rules takes a lot of time.
Hope this helps.