My understanding is that at the start of a game, the system shuffles and draws three hands for you, and then selects one of them to be your actual starting hand. I don't know what heuristics it uses for which of the three to select, but typically in real life you would be hoping for three lands as a baseline, ideally that can tap for the colours of the spells in your hand as well.
I believe this only applies in best of 1 matches, but not best of three matches.
Unfortunately I don't have a credible source for this.
You can, but it doesn't help when your next hand is exactly the same, or the opposite problem. There's been times I mulligan down to 1 card and see nothing but land the entire way through. Probably in the same match, the opponent mulligans down to 3 cards just to get 1 land.
It's bad enough that my friend group casually accepts having to "concede" 2 or 3 times just to get a decent match going.
It does, you can shuffle and draw a new hand but then you need to put a card from your hand on the bottom of the deck (you can repeat, putting two cards on the bottom, then three, etc.)
Card advantage is massive in MTGA so people don't mulligan when they should ...
I believe this only applies in best of 1 matches, but not best of three matches.
Unfortunately I don't have a credible source for this.