Betta - air pump yes or no?

I don't think he will hate it. He may even like it but it is not necessary.

I don't know that he will hate the bubbles, but IME bettas are not all that fond of a lot of motion in the water. They tend to like more still waters from what I can tell and what I have read. Won't hurt to try it and see how he reacts, but it might be something you end up taking out. I had to take out my sponge filter I had in my betta tank since it created too much surface motion and my female CT def didn't like it.

It depends on the personality of the betta. Some like them and will play in them, some won't.

In my opinion, the majority of bettas prefer calm still water, as like their natural living habitat.

I've had a lot of bettas, I put an air stone in all of their tanks and none of them really seemed to mind it. It does depend greatly on the personality of the fish, a friend of mine had one and it viciously attacked the air stone so she had to take it out. I find that if you are getting it from a box pet store, they are just thrilled to get out of their dirty little cups most of the time. You can always try it and take it out if you find he/she is not pleased with it

i would say no. it's not really necessary. In a 2.5 gallon tank, it would add a significant amount of current, which the betta probably wouldn't like. Just monitor the temperature closely because small heaters in my experience are pretty unreliable.

You said you already have a filter. There is no need for the air pump. For once bettas breathe through the surface so they don't need oxygen rich water like other fish. That's how they survive in those cups. Filters are important to keep the water clean but the bubbler is overboard. I would just go without it. Less clutter in the tank.

I keep a air pump in all of my tanks including the bettas, none seem to mind it in fact I have one that enjoys napping next to the bubbles. Depends on the betta but it certainly won't hurt them.

The best use for the air pump is to run a sponge filter. Turn the bubble exit flow towards the side glass, to cut down on current.You can eliminate that external filter, with its strong outflow. Floating plants make bettas comfortable: try Water Sprite, the thicker the better. When new plants form, you discard the big old plant: plant-based filtration!