Mass-effect – During the Priority Mars mission do the waves ever end

I can only speak for Bronze rankings. For this type of mission depending on which wave it is you will get stronger monsters that spawn plus the trash monsters. After the stronger monsters are dead, the trash monsters will never stop spawning, they will also continue to spawn in the same area until your team moves to a different area or completes one of the 4 disarmings.

I have done this a few times with reapers as an enemy, I forgot which wave, but there was 2 banshees and 2 brutes and 3 or 4 ravagers. After all those enemies were dead the only monsters that continued to spawn were cannibals and maruder and rarely a few husks would come running.

I forgot the numbers now and dont have it in front of me at work, but I think 8 enemies can spawn at once and only a maxium of 2 spawn points at a time. So from what I have seen, no facts behind this. So if you know where current spawn point is you can run the backways around the map as they head to your last location (as long as you dont shoot) and than can get the next objective and never have to shoot at the trash, and until you kill the trash more wont spawn.

But I have stood in the same spot for 4 minutes with a sniper rifle and let them run down the hallway and killed 20-30 monsters in the 4 minutes because spawn point didnt change because I did not move. 4 minutes ended, my mission ended, but got like 20k score.

No, you can't catch her. As a Vanguard, I used Charge to stay within 0-5 meters of her through the entire chase with no effect. She will always reach her shuttle and trigger the cutscene that follows.