What kind of hose is it and whats the damage?
 

Ive owned this awesome 2008 a3 sportback for a year and half. I was changing my cold air intake. I must of pushed to hard on the intake, because it snapped the hose and pinkish-reddish liquid came spewwing out. It must be either coolant or transmission fluid. But I really have no idea. Would really appreciate if someone could enlighten me on my issue

I'm not 100% which hose but it could be the coolant hose to the radiator. The picture is in a strange angle but I'm guessing you took it from the front of the engine, leaning over which is why I see a fan in the top portion of the picture (if I'm not wrong).

Anyhow to answer your questions:
1. This was coolant
2. As long as you don't use the car - you'll be fine. Simply replace the broken part, fill her up with coolant and burb the system (since you introduced air into the cooling system).
3. Again if I interpreted the picture correctly it's part# 4 in this diagram (coolant distributor):
https://genuineaudiparts.com/parts/2...&siteid=214407

+1 on that. For sure it looks like the radiator hose. If the nipple is still in the hose that broke off you can try to pry it out and use some epoxy to repair it. I know it's a haggard way of fixing it, but if you need to get it driving that's the best way as a quick patch.