Huge spoilers if you haven't watched the rest of the series--->

Nobody knows, but we can speculate that mikkel's life continues and he'd probably do what the rest of the other characters do. His death was mostly out of his love for Jonas and we could assume that mikkel would probably try to protect Jonas.

Also if Adam never sends Jonas to save his father, Jonas doesn't become close with Claudia and then Adam never exists because Jonas was stuck in 1888 working closely with Claudia which made adam exist in the end.

If Adam doesn't exist then the whole knot doesn't exist. There is no origin so we can assume that Adam/Jonas have all of the power over mikkel's suicide and they are the reason behind it (besides fate in general). If they were to actually stop mikkel's suicide (which has been shown to be deemed impossible infinity times in Jonas's case) then the knot would never form and time would never fix itself in the finale. Big determinism right there.