I've run around 4 short evil campaigns; 3 one shot evil and a decently long evil campaign involving the rise of a new demon lord in the abyss (that was really fun). And before I offer my advice I will first tell you the books you must must must read before doing an evil campaign; book of exalted deeds (good to counter act the evil and such), book of vile darkness (you just can't have an evil campaign without this thing), exemplars of evil (the guide book to villainy), and then depending on your general theme and setting I can share the name of other books.
1. First off villains don't "need to do something" while its true you can't have a "passive" villain you never truly have "passive" PC's either, think about it hard enough and you realize the death of a campaign is usually when the PC's wait for adventure to come to them instead of going out and seeking it themselves. It's hard to explain but just because their evil doesn't mean you have to treat your PC's differently in fact it gives you a chance to throw some of the awesome good aligned creatures at your PC that they usually ally with as a good party and gives them a chance to make deals with evil creatures that normal good PC's can't cooperate with. Betrayal by trusted friends, things not going as planned, being hunted by somebody/some organization for your actions things that happen to normal PC's happen to villains all the time.
In the end being evil requires more cleverness and observation of what's happening and has happened than one would think everybody thinks an evil campaign is I kill who I want when I want and how i want to when it is actually an interesting chance to use your skills, spells, and role playing to manipulate those around to doing what you want for you. Good quote I got from futurama and used for a villain in my campaign who had manipulated the city into believing the PC's were villains who planned to destroy and loot their city, "If you do things right people won't be sure you've done anything at all."
2. Minions, allies, underlings, whatever you wanna call them are always a tricky business for us as DM especially when we allow our PC to essentially have control over NPC's. You as a DM need to be able to figure out what it is and isn't the PC should be allowed to do with people that are his followers, I mean think from the position of a minion, would you jump into the spike pit so that your master could cross safely over your remains (only if your his thrall lol). Typically if you follow the rules of the leadership feat, keep in line as to what even an NPC has limits on what they'll do, you should be fine. Hell use their minions as plot points while you're at it, not all minions are faithful and not all people who join under you are there to help; spies are frequent in the world of DnD as are assassins.
Also keep in mind a minion should never do anything as good as a PC (except as a corpse to hide behind-even bards have their uses lol), minions make mistakes especially if you rely on them too much and if you're PC's do that make their mistakes obvious one ex. forgot to set up the acid pit trap for the lawmen pursuing you for crimes etc.
You can just outright now allow minions if you want (remember you're the DM) in the long running evil campaign they were the minions of the rising demon lord and as such he forbid them from contracting those to work under him without unless he sent them on a mission where he assigned them underlings (quite a few of those). Worked out well since the PC's only had minions when they really needed them or when I could plan for the minions in part of the plot and combat.
3. If this hasn't been a problem in a good campaign I am actually surprised. There is always and i mean always character conflict because nobody (in or out of character) carries the exact same belief and ideas and even then can ever truly agree that one thing is how it should be or that one way was the right way. Character conflict is a beautiful double edged sword that allows for character development and interesting plot changes. As for "us against the world" as Dalar said if you come into a campaign evil/chaotic aligned in a mostly good/lawful world you get fair warning and undoubtedly expect a few scrapes and bruises along your journey.
3. PG-13, I guess this is different for me than most people since when I purchased the BoVD it became my go to book of what to throw at hot shot players who thought they were untouchable. The tone and degree of description and violence that you should allow should be based purely on who mature and capable your group is of mentally handling these things. For instance in one of the one shots the PC half-giant half-orc had a profound hate for elves and upon discovering a small elf camp slaughtered, skinned, and turned them into his new clothes for the week (the details were left vague for this instance because there were women present who probably couldn't have handled the chilling detail I can go into as per example 2). Example 2 involves a Halloween special where an NPC elf (irony) former slave who had developed a grudge gone sadistic murderer intent towards his captors, humans, that led him to capture and torture them for days as they begged for him to kill them which he made the PC's full aware of during their pursuit and capture of him (my PC's made sure after this incident that I ran the horror themed one shot for next Halloween because as one of them put it the next day, "If this campaign involved insanity points I probably would have hit max halfway through and that's not my character that's me and that was before we entered the guys hideout."
I find that it's best to adapt the degree of horrifying detailed based on what is necessary for the campaign obviously if this is more of an evil horror themed campaign details shouldn't be spared since the point of the details is to add depth to the tale. If we're talking about what I did for the evil campaign details were conservative, things weren't overly gory, and all in all I treated descriptions with as much care as do during any other themed campaign; as much as need and a hint of flavor when the time calls for it.
4. Though we'd all like to be a PC like Richard in LFG I find it's best in any campaign that the players have some drive, rather it be the demon lord who has promised you high positions in his new kingdom for you loyalty or some other thing I can say that without a drive a campaign will die. Beyond the point of evil for evils sake looks in exemplar of evil that book is just gold.
If you need anymore specific advice just message me and I'll get back to you in a week or so.