There are a bunch of considerations here. This gets super technical. I am not a doctor. I've had two babies, one totally normal, one crazy high-risk emergency. In between those, I had one miscarriage. I wound up seeing doctors at three different hospitals (as well as midwives at one of those hospitals) over the course of these pregnancies, but because of where I live, all of these hospitals were teaching hospitals of Harvard, which means they all had certain policies in common. Things may vary for you.
I think it's worth discussing with your midwives what conditions would risk you out of the birth center, and how that would be handled. I have heard of women being referred out because of changes in midwives insurance coverage, for example, and if you're dealing with a basically bureaucratic change, you probably want to go ahead and agitate to keep things as close to your birth center plan as possible. If they risk you out because you're showing signs of pre-eclampsia, because you're GBS+, or because you have gestational diabetes... you get into a place where some of the procedures you're concerned about become solid practice.
You also want to know where they'd send you if you risked out, and what standard policies and procedures are there. You want to know how they staff L&D. Is there an anesthesiologist on the floor? Will you be seen by the attending physician on shift when you're in labor, or will they page your doctor? Your odds of having a natural delivery are actually higher when there's staff on the floor, because you can take a wait and see approach if monitoring is revealing variations that might indicate trouble later. If they have to page a doctor in, they'll pick up that phone the very moment they think things might be diverging from normal, and you can wind up with an OB who doesn't want to have wasted a trip. Whereas if the doctor is there, they can wait to start the emergency moves until there's an actual emergency. The problem is, having staff on the floor all the time is more expensive then paging doctors in on an as-needed basis.
You also want to know what the hospital's insurance allows them to do. Can they do vaginal breech? VBAC? How often do these things happen?
And then you just have to pick your hill, and decide whether it's worth dying on.
Hospitals tend to kick up a hell of a fuss about monitoring issues. They want you on the monitor. The paperwork you are going to have to sign to not be on the monitor is the scary "your baby might die" paperwork. If anything goes wrong, the monitor strip is going to come up as a discussion point, first in the hospital's morbidity and mortality review (where the staff on your case are going to be grilled up down and sideways), and then in depositions and in court (if you or your baby are injured, you're going to need money, so you'll sue). Mothers hate it, though. It's annoying to have on, and it can mean that everyone's frowning at the monitor strip while you're screaming through contractions. If you've been risked out for a basically bureaucratic issue, there aren't special concerns about placental function, and you are not getting an epidural, you can probably convince them to go intermittent on the monitors (although it's my experience that "intermittent" means "fifteen minutes out of every hour", which can be more annoying then just leaving it). Some hospitals have wireless units, which make it easier to walk around and do what you want, even with monitors. No hospital is going to leave a nurse in the room all the time, and they don't padlock those babies - you can just take it off ("I needed to use the bathroom," or whatever).
The IV is another one they're going to fight for. You want to be able to use your hand and walk around; they have nightmares about trying to get venous access while you hemorrhage. The standard compromise is a hep lock (not a ton better, in terms of using your hand, but at least you're not tied to a pole). I hemorrhaged after my son was born, so I'm kind of with them on the hep lock.
The hospital gown - dude, so long as they can get to the things they need to get to, you should be able to wear whatever the heck you want. Anyone who says otherwise at the hospital is powertripping. BUT. They might quite reasonably offer you a johnny so that you don't ruin your own stuff (or after your water breaks all over your own things). Labor is messy, and afterwards, the staff just sweep everything up and bundle it off to be dealt with by their linen service, which means that if your stuff gets caught in that sweep, you're never going to see it again. All of the hospitals I've been in have been perfectly happy for me to wear my own clothes as long as they weren't doing surgery, as long as there wasn't blood or feces on them. Once you have blood or feces, their prejudices kick in in favor of "clean", and they want it gone. I strongly recommend laboring in their stuff. Save your things for after the baby is born. (But if it's a situation where, say, you have a history of childhood cancer, and you throw up as soon as you put a hospital johnny on - no joke, some people do - no johnny for you, but stock up on cheap pajamas so you have extra sets of things you won't be sorry to lose.)
The wheelchair to the door - on the one hand, what are they going to do, kick you out? Great, because you're trying to leave! On the other, it's two minutes in a wheelchair, is it going to kill you? Do whatever gets you home fastest, with the fewest insurance hassles.
Eye ointment, and delayed clamping are issues where you're going to have to feel out the culture. Baby on the stomach is partly a culture thing, partly a thing where it depends on the situation. I hemorrhaged after my son was born, and couldn't safely hold him, plus, they were using that space for uterine massage. Have a backup plan on this. The classic alternative is to have your partner cuddle the baby skin to skin.
Congratulations on your pregnancy. I hope all these concerns remain theoretical.