@andy:
If you tame an animal, it loots as any other mob (so most time no loot, lol

). What was meant above is: if you try to tame 5 times, you will just decay your whip more than if you would kill it instantly. On the other hand you get taming skills for each attempt, no matter if successful or not.
@Kujo:
The TT reflects how much nutrio bars your pet has currently "on it". Training costs additional food, so training will decrease the TT of a pet

.
If you want to place it in your apartment, you need to have 30 PEDs TT on it. So if you feed it 30 PEDs, then leave it for a month in your apartment and you want to replace it, you have to feed it again, as the TT is then below 30.
I hope, this helps a little, if not, feel free to ask (or call me on XFire

).