Tubes are more durable than bands, but less efficient. I don't know why exactly; my guess would be that the air inside the tube has some damping effects. I've never hunted with a catapult but my guess is that you'd want efficiency over durability since you are (hopefully!) not taking many shots. Tubes might be better kept for plinking.
Theraband Gold is the best elastic I've tried. It's that stuff you get for physiotherapy. That particular one is considered by many to be the best and it can be bought in long rolls. £30 for a lifetime supply. It's easy to cut your own bands (DO buy the proper cutter) and it's great fun to experiment with different lengths and tapers.
Straight bands will last a little longer but sacrifice efficiency. Bands which taper towards the pouch are more efficient but less durable. For a hunting band, I'd again imagine you'd want the most efficient you can get since you can cheaply replace them if they break and always carry some spares.
For ammo, I bought 1000 10mm BB's for £12 on ebay. If you manage to collect 50% of everything you shoot that's 2000 shots before they're all gone, or 0.6p per shot. Pretty good imo.
There is indeed! Joerg Sprave of the Slingshot Channel on youtube has made an excellent band calculator. Just plug in your specs and it'll tell you the dimensions. The key is to use a sharp roller cutter onto a cutting mat. Scissors, scalpels etc leave little imperfections which will be the weak point at which the band eventually breaks. The cleaner the cut, the longer the band will last.Is there an idiot's guide out there as to how long to make your bands, how wide to have them and how much to taper them? (I'm sure that there are lots of subjective options but a good beginners choice without having to do lots of experimentation)
I seem to recall that attachment is just by wrapping the bands with offcuts of the band?