this is certainly possible. It can always be assumed that npc's grow and develop just as well as the pc's do. It's best to try to keep the villain's advancement rate approximate with the pc's. So it wouldn't be suggested to have an npc with lower levels than the pariy the first time they meet suddenly be much bigger than the party's APL the next time they run into each other.

Of course, it could also be assumed that they have money to stay in a location for longer periods of time and train in their class abilities, making advancement much faster

This pertains to D&D 3.5, but a bit into 4e as well.

The rules for obtaining feats have always kinda bugged me. Considering the sheer volume of them in any one source book is staggering when compared to the total number that you can have from leveling. I was wondering if it might be a good idea to add two additional ways of gaining feats; learn to earn and XP buy.

Learn to earn would entail that you find a way to have the feat taught to you (instruction manual or a teacher). Perhaps you could set up skill challenges for them to complete, like researching in an appropriate library for metamagic or bardic feats, enduring extreme temperature checks for a set period of time to gain heat/cold endurance, or dueling an instructor to submission using two weapons to gain the two-weapon fighting feat. Of course, a DM would have to set a time sacrifice in addition to the teacher requirement so that people wouldn't just spend the whole first level just spamming a dojo, and it could really only work with feats that can be taught. This would encompass ones like combat reflexes or power attack, but exclude most racial/biological stuff like Abyssal Heritor feats or Racial Emmulation.

The XP buy would be applied to all feats, but cost XP (obviously). I got the idea from the Fiendish Codex I, which has a spell that bestows Abyssal Heritor feats for 250 XP. For this I'm unsure what a good cost system would be, since it has to keep feat obtaining reasonable. Would 250 flat be a decent amount?

If anyone has any suggestions or advice, please message me!

250 flat is a bad idea, at least. A first level character could choose not to go to level 2, but get 4 Feats instead.

Why not just give them bonus feats at certain intervals?
Give them a bonus feat at every even level. This only takes some of the benefit away from being a fighter, whose main thing is feats.

XP feat buying is something I've thought about very much, as I'd like to implement that if I ever come to run a game. But do it like they do it in e6 games: 5k XP for 1 feat. Prevents feat-loading at lower levels, while being more or less balanced throughout the rest of the game.

Getting trainers is quite cool version too, specially if you enjoy building up NPC's. Just go around with them and give them odd feat choices or spread some rumours about that character who could hit a target with anything you handed him, provided he wasn't very far from it (voilá! Learn Throw Anything feat).

You could also give more feats to the players for free. I think most classes (specially Core ones) get too few feats for my taste.

You can also give feats based on RP. That's quite welcome among players too.

In Pathfinder or 3.5, are there rules or a system or rolls when a character is going fishing or hunting? Or even based on what they use for such actions? Like when they go fishing, does it matter wheather they use a fishhook or a net?

3.5 Survival has rolls to live off the land that presumably include such activities.

I find that I'm a little too lenient with killing off players, although it's happened with no great degree of anyone getting upset, (there was good reasons why their characters died) its been mentioned to me by some of my veteran players that I'm a pretty gentle DM. And while it's not been a problem I worry that I'm not having harsh enough consequences to poor choices made by the players. Anyone have some tips for keeping a better balance?

Sometimes actions have consequences. Let them learn that the hard way. Botched heals that leave a penalty (such as a broken leg that leaves a limp) that can only be corrected by having a a higher level healer-type redo it (at a price), or by re-breaking it and having it healed again. Wanted posters out for rogue-types who get spotted. Friends of the people they took out who want revenge. Attacks targeted not on them, but on their equipment, so as to take out their support structures. *Then* you can enjoy the looks on their faces as they go to use their healing potions (or whatever analog you have) only to realize that the liquid dripping from their backpack happens to be... you guessed it, their potions.
You don't actually have to hurt them. You just have to shake them up a bit, take away the crutches that they lean on too much, so that they start to think of what would happen next time they blithely go into a dangerous situation and find that the support they rely on just might not be there.

When a Published Module says I award the party XP for completing a Story part (Like for example, 1200 XP) It doesn't say whether each character gets that or that gets divided up among the players like in an encounter. Which is it?