Ok, make sure you buy a dechlorinater and add that to the water BEFORE you put the betta in. Also, for the next week you are going to want to do a 10 - 20% water change with dechlorinated water every day. After that, you will only need to do a water change every week. You should let the tank run for 24 hours before adding the betta, though.

Yes, float the bag in the water before adding the betta.

Good luck with finding a betta!

ETA: Have you found a tank yet?