Do you know were I might be able to find a fitting to connect the RO line to my bathroom sink? Also does any one have any ideas about what to do with the waste water?
this is what you want for the RO to connect to the plumbing under a bathroom sink.
INLINE UNDERSINK SHUTOFF ADAPTER
http://thefilterguys.biz/fittings.htm
anyone selling ro parts probably has something similar.
for the wastewater, sending it outside for a garden is about the best, especially if it's automated. but you probably won't be using so much water that it'll be that big a deal. cut your shower a minute or two short most days and you'll probably save more water than you waste.
would it still work if I just poured warm RO water over it every week or two?
maybe. but it only takes that one clump to keep it from sealing. though to be honest, if it fills up over the float valve, it'll be putting alot of pressure on the gasket, which would probably be enough to bust the kalk clump and get a seal again. dunno, but it's best not to tempt it.
How do you wire the relay to the perstaltic pump?
depends on the pump. your hospital pump probably has a backup battery, which means you can't simply toggle the power on and off to turn it on and off. some have this bypassed, you may be lucky with yours. or you could forget the float switch and just manually tell it how much to dose per day (just like a litermeter). you'll just need to keep an eye on it and adjust it ever so often (much less often than you'd think).
if you do want to float switch it, and if it does turn on and off when you toggle the power, and not lock up in an error mode, then go to radio shack and get a 120v relay. relays are incredibly simple, the basic ones have 4 pins on them. 2 of them power an electromagnet and take the low voltage (9 or 12v usually) to activate it. this throws a switch inside that opens or closes the 120v circuit. so, use an appropriate power supply through a float switch to the relay. then wire the 120v pins to an outlet or chopped extension cord. you won't have any trouble with it.
I have this hospital pump ^^^. I couldn't ever figure out how to work the thing

.
you need to get a dripset for it. it's a piece of tubing with stop-blocks in it to hold it in place with tension around the rollers.
But I got the feeling that it only doses and relies on gravity so I figured it wouldn't work for this application. Is it the same thing as a perstaltic pump?
if you find a dripset it should work. it is a kind of peristaltic. i prefer the regular lab ones though. the medicals rely on tension around the rollers to pinch the tubing (which cases the tubing to stretch over time and usually last 2-3 weeks). the lab ones squeeze the tubing between the rollers and a fixed wall and the tubing lasts years.
For the solenoid do you have to have a relay for the float valve to signal the soleniod.
if you get a 120v solenoid, you just wire it to an old plug and plug it right into a timer. nothing to it. do a quick search to see which one the cool kids are using these days. i got mine years ago off mcmaster.com for 20 bucks.