Most likely, yes. Especially if they are aggressive fish to begin with. 2 mild mannered fish might co-exist, but you'd run the risk of them fighting more as they matured, ending up with one dead fish, if not losing both.
Depends on how long the tank is (not gallons) and the temper of each fish. One must realize that most bettas are now bred for show and not fighting, so some modern strains are actually more docile than their wild cousins. Now that I have said you can keep two in one tank 125 gallons is probally too small unless it is a shollow but long tank (around 10+ feet long.)
yeah kinda like cichlids. The more there are the less agression because the fish can't concentrate on a certain fish. not saying to overcrowd it but stock it healthily!!
I dont think it will matter as as soon as they begin to fight they have a tendancy of fighting to the death right then and there. I used to breed them and as soon as the young males started to show real colour I had to separate them or they would have constant battles and would stress eachother out so badly that they would die.
i had them in an outside pond probably 10 square feet heavily planted and they found each other and fought. but then i kept two in a gallon tank together before too