1) Water Test Kit
First things first, you need a water test kig. If money is an issue, and you have a PetSmart around you get a
5-in-1 Strip Kit and the
Ammonia Strip Test both from Jungle Labs. Ad them to your cart, print it, and take it to the store. You'll have what you need for under $20.
2) Algae Problems
You mentioned algae probs, is your tank in direct sunlight all day? how long do you keep the lights on? IME to keep algae under control, your tank should not receive more than say 10 hours of light per day. You should also keep it out of direct sunlight.
3) Salt
I do not think adding salt to the tank is a bad thing just be carefull how much you add and where you add it. You have a 2.5g make sure it does not land on your fish.
4) Water Changes
These should be done weekly. General rule of thumb is 25% at a time. If you are doing more because of algae, get a small algae brush. That will help big time.
5) Betta Fighting
I don't know if I read this right but are you letting your Betta fight?
6) In the mean time...
rrkss will like this one. After water change, salt, and what not, you can try to help the poor guy along by temporarily adding an airstone to the tank. The extra oxygen will help the poor guy "breathe" better.