1. I'd say there is a subset of the medical profession that focuses on treating Kaiju Blue related illnesses, particularly in the the cities/countries of the first three Kaiju attacks. Exposure in the past would only be detrimental for a person looking at the Jaeger Academy if it has a lasting ability to impinge on their ability to perform. If they've been given a clean bill of health, they'd be able to stick with the program, but will be told up front that they're required to check in more often to ensure they're remaining healthy and stable.

Someone who is unable to hold up under the physical duress would be considered very carefully only if they were also an extremely promising candidate, but by and large, if you can't keep up with the big dogs, you're left on the bench.

Individual pressures from family or staff met initially in the testing facility are welcome to cast further doubts and create an atmosphere of questioning ability for any given character. The question of "Will they be able to keep up?" is important! That point will be driven home early on.