My betta <3

[sportygirl]

I just got a betta a week ago a rescue betta from poor conditions at the store but seemed to have no obvious damage. And now appears that his small fins ( i think they're called pectoral fins) are transparent on around half of each or just plain missing a chunk of those fins! Is this fin rot? and how can i help it? I also have some questions:
1. Is there any way to make/influence my fish to make a bubble nest?
2. How can i teach him to jump and push a ping pong ball, i have tried but failed repeatedly :(
3. I've heard and read that bettas love resting on plants near the top of the top of the tank but he only seems to like always lying on the rocks or where there are no rock on the bottom, is this normal?
4. And what name do you like the most :P ? Tango, Moon, or Jude??? Thanks!
And heres my betta and tank ( before i got the heater) its 2.5 gal and he seems to not like the cave/barrel or is still getting used to his new surroundings!

[ChoclateBetta]

betta fish love live food plants and betta log my betta fish loves it.

[LebronTheBetta]

Clear pectorals are fine, Lebron has a clear one. You can't make a Betta make a Bubblenest. It's not because they're happy, they're just protecting territory or ready to breed. Just hold a piece of food over him and he should jump. For the ping pong, not sure. If he's curious enough he should. You choose his name, remember it's a boy.

[sportygirl]

ok thank you! I wil ltry holding the food above and im still deciding on the name!!!