Whew! Quite a lot on your plate, but nothing that hasn't been seen and experienced before. Congrats on taking on the DM role. As you see, it is a lot more work than it looks like from the outside! I've been playing and DMing various systems off and on for a little over 20 years. I'm not the best or the most experienced by far, but if you're willing to read, I'd be glad to offer what I can to your situation.
1) The being in charge thing takes a LOT of getting used to. Sounds like you've an additional issue with your stutter. First, kudos for admitting up front that's a problem for you. I am nearly deaf and rely on lipreading. My friends know this and over time have become very aware that they need to face me when they're telling me what their characters are doing. It slows things down a LITTLE, but it's gotten to the point where it's not a big deal anymore, and they understand that there are times when there will be misunderstandings that need to be worked out. Having a map/grid to keep things visual really helped-cut down on the need for asking and explaining how far away X is from Y, for instance. My experience has been that gamers are a wonderfully adaptive group, and I suspect, or hope, that the same will be true of your gaming group. Give it a little time.
2) The party refusing to buy books is the same age old problem of leading a horse to water, but not being able to make it drink. Given your age, I assume that most of your group is teenagers, and that usually means there's a cash flow problem. Look into used bookstores. I have one nearby in a college town that I raid regularly for gaming material. (Bought my old First Edition Handbook, before it was the First Edition, of this game's predecessor there....) There's also a number of websites that specialize in selling and auctioning things. The bottom line, though, is that there need to be more rulebooks in your group, and I'd recommend you gently point that out. It comes down to "we can spend time flipping through pages, or we can actually game." To an extent, it's also a problem of learning a new system, and that aspect of it will go away as players become more familiar with the rules. Worst comes to worst, start playing with a timer. If someone needs to check the rulebooks, give them sixty seconds before they lose a turn. Just remember to explain that you're not doing it to be a cruel SOB-you're just trying to make sure that the maximum amount of fun is had in the short time you have. Hopefully it won't come down to that and the players will be able to pick up a cheap book somewhere.
3) Diversity of the party, yup. You can force the players to toe your line and see how that shakes out, or you can call them together and explain your situation. Tell them that you'd like to run X type of adventures, but that you're willing to alternate with controlled insanity or smash-and-grabs. Maybe you could even have your players roll up 2 characters-one for the serious adventures with roleplaying, and one for the exploding monkeys.
4) Difficulty- Without actually being there and seeing how your group is handling things and the situations you're putting them in, it's hard to tailor any specific advice. However, you can always fall back on a few things. If you're using base level statistics from the bestiary, for instance, change 'em. Give your critters more hit points, a higher armor class, etc. Remember, too, that the average encounter is only supposed to drain about a quarter of your party's resources (assuming you're using published game material.) In the instance above, perhaps you could have thrown in a wandering patrol at a critical moment. As the DM, it's your world. If your party is wiping the floor of 5 goblins, maybe next time try 7 and see how that goes. Is your party over-equipped? Do they have too powerful gear for their level? Rust monsters and oozes can be a good fix for that. So, too, can the ethereal filcher. But, in all honesty, if your party is overpowered for their level, then I'd start throwing bigger and more powerful opponents after them before I started arranging for them to lose items. Creative parties are something that EVERY DM has to deal with-usually for the better, in my opinion! If they're going to challenge you, challenge them right back until you find a level of difficulty that works for you. Like I said, ramp it up slowly until you find a sweet spot.
Please also remember
1) The more you do this, the better you get. In five years, you'll look back and want to slap your self for worrying about any of this.
2) Generally, slow changes in a game are better than fast, immediate dictates from you. No one likes to be told "Thou Shalt Not..." in their own fantasy game.
3) When in doubt, talk to the players. It's not just your game or their game-everyone's in it together.
Best of luck!