I'm planning to have my third homebirth, second time in water, with my midwives and husband present. If all goes the way I HOPE, my mom will also be here to look after our boys, though not in the birthing room — that's just not her thing, and not really mine, either. (That will depend on when/if she goes back to China after the summer. She and my dad lived there this past school year so Dad could work as an administrator for a school and plan to go back again next school year, but she's mentioned staying here longer to help me out and then going back later in the fall on her own. She's nervous about the travel aspect on her own, though, so I'm trying hard not to push her one way or the other. Anyway, that's the backstory to THAT!)
From my own personal experience, the water birth was GREAT. I found the warm water to really help with the pain, so I'm definitely trying for it again. Meaning, we will set up for it, and hope I make it in the pool in time! Last time, I think I only spent about an hour, hour and a half in it all told, because my labor moved so quickly. No complaints about that! But we'll just make sure to fill it sooner this time. I'm not sure if I'll be renting the pool from my midwives or purchasing the equipment myself like last time. It will depend on cost; if I can do it cheaper myself, I'll go that route and then try to re-sell the stuff. That worked out nicely last time. (If you are planning a water birth, I highly recommend a thread on here all about the equipment you need. http://www.mothering.com/community/t/589333/birth-pool-resources-and-information)
Aside from pain relief, I liked that I could easily get into more positions while in the pool, and it was nice to hang off the edges. And then my son was born, still in his caul, and that was really cool too. The midwife pulled it off of his face and out of the water, and then we sat in the pool for a little while with his head out till the cord was ready to be cut. I liked getting out and going right over to my bed without feeling too dirty. Now the clean up, on the other hand, was apparently not fun! LOL. My husband had quite the time getting it drained. That was a downside. It might have been the hose we used, though. Not sure. But it's a sacrifice we're both willing to make again, because the good definitely outweighed the bad.
I'm not sure about where you live, but here in Ontario, you can walk out of the hospital with your baby within a couple of hours of birth under a midwife's care. As long as there were no complications for either of you, that is. I'm not sure what policy they have if you're under an OB's care. I would not want to stay for three days, either, so I don't blame you. Look into that for sure!
As for what a midwife does and doesn't do, I'm going to assume you mean in labor since that's the topic? Again, I can only speak from my own knowledge of our system here in my own province, but basically they act very much like the nurses would at a hosptial, as well as the doctor. They check on your stats periodically, and on the baby. They take your vitals and check your dilation. They coach you as needed, like suggesting positions to move into and how to breathe, and do things to keep you comfortable, like wiping your brow or getting you a drink. They will catch the baby (if you or your partner want it that way, that is) and check the baby after birth, but they don't whisk it away to clean it and weigh and measure it. They let YOU hold the baby first, and for as long as you like as long as there is no medical reason to take them away for oxygen or something. (I was a bit surprised by the lack of "cleaning up" the baby after my first birth, actually, but many sources suggest that it's totally unnecessary for their skin. Just wipe them down with a soft blanket and give them a real wash later on.) They deliver the placenta and deal with that. When you've had some bonding time and a chance to try nursing, they will then measure and weigh the baby (with the awesome, hanging fabric scale thing only midwives seem to use). They will help you get cleaned up and provide after care, like stitiches, if you need it. They'll help you get settled comfortably and get the tylenol and advil started (those are necessary for me almost right away, especially with #2!), and bring you food if you don't have anyone else to do it. Then they settle somewhere in your house to make their notes and give you private time with your new family. They usually stay for about three or four hours, to make surre everything is going well, and then they come back the next day for a check-up. They come back on days 2, 4, and 5 or 6 during that first week to make sure things are going well, administer any post-natal tests you might have agreed to (like the heel prick test) and just to generally answer questions and help with breastfeeding. They get you to keep track of the babies urine and bowel outputs to make sure that's all going the way it should, and weigh them each time. They check on you, if needed, to see how you're healing. Then you see them again in office about two weeks later, and the at six weeks post-partum.
At least, that's the way they do it here in Ontario! And I love it. That at-home attention in the first week is so invaluable. It means you don't have to go anywhere, yet you're very well looked after. I'm always very sad when we get discharged from their care.
Education-wise, I found them to provide answers to questions and so on, but for birth and labor preparation, that was mostly on me. I read lots of websites, books, and birth stories. Didn't end up taking a class, but felt pretty well prepared even without it. Indeed, I don't think I missed out on anything I couldn't have/didn't find out on my own anyway, but I certainly don't think they hurt if you want to take them!
I hope that helps answer some of your questions.