What happens if opponent has infinite turns, but cannot kill me because I have infinite life?
Your opponent cannot win, and forestalls losing to Walking Ballista by looping Nexus of Fate. Therefore, you would win the game either by direct judge decision because you explain the inevitable sequence of events, or by the judge forcing your opponent to let you draw cards and eventually getting you to the Walking Ballista.

There is clearly a loop happening. Remember that "game state" is not a defined term. Even gaining and losing life does not alter the game state if it foreseeably does not decide the game at any point, as is the case in your scenario.

Case 3 of the answer to the question you linked does apply. Your opponent can propose a loop with any (finite) number of attacks, and you can counter-propose the same loop, except you first gain enough life to survive all those attacks. Then a significantly different choice has to be made, i.e. your opponent must let you take a turn. You will eventually draw your Walking Ballista and win.


  721.3 Sometimes a loop can be fragmented, meaning that each player involved in the loop performs an independent action that results in the same game state being reached multiple times. If that happens, the active player (or, if the active player is not involved in the loop, the first player in turn order who is involved) must then make a different game choice so the loop does not continue.


From the tournament rules:


  The judge is the final arbiter of what constitutes a loop. A player may not 'opt-out' of shortcutting a loop, nor may they make irrelevant changes between iterations in an attempt to make it appear as though there is no loop. Once a loop has been shortcut, it may not be restarted until the game has changed in a relevant way. Proposing loops as an effort to use up time on the clock is Stalling.