It may have been a rumor that said you can get Master Balls for training the Regi trio, but always assume these are false. You cannot obtain Master Balls by training any Pokemon to level 100. You can obtain more Master Balls by going into the Lottery in the department store of Lilycove City or Lumiose City in X and Y. This is very rare, but it is definitely possible. If you are playing the Generation XI games, you can play the mini game called Mine Cart Adventure on Global Link to possibly win a Master Ball as well.
only one after you beat the elite four
You can get only one per game.
Well, first you have to sit through the credits. Then you can go catch Latias, find the Regis, complete your pokédex(after you do, you can get a starter from a different region, I cant remember which one), go for the Battle tower, train your pokémon to level 100, try to beat the Elite four as many times as possible, etc.
Yes as many times as you want
It all depends on how you train them. How many Rare Candies and other drugs such as Calcium and Iron you've given them can determine their stats. It also depends on what moves you teach them, what level they're at and even things like their nature. Every Pokemon is unique, even if you train them in the same way.
Victory Road, just before the Elite 4. i don't recommend going there because tons of wild Pokemon pop up, and there arnt that many trainers. sometimes i train my 40's on 3island
One, although if you have the AR cheat, 999 masterballs can be acquired.
That depends a lot:* What you want to train for * To what level you want to train
Infinit
1
one
there are 3 regis. EXCLUDING regigigas
only one unless you cheat
only one. unless you trade with other versions that have some (as in Pokemon holding masterballs and then trading it to your game)
37 miles
You can get only one per game.
You can get one for sure, like in all games. But you can also win Masterballs from the Lucky Number Game if all your digits match.
INFINITY MASTERBALLS just do my trick Trade pokemon for pokemon holding masterballs take them away and trade for your pokemon back