For the first question, we'll leave that up to the discretion of the players. The ship is stocked with a wealth of doctors and scientists who can cure just about anything, but not everything, and it's expensive to go to them. Alternatively, the wormhole that brought them to the ship will have affected the character in such a way that they're magically cured (or not, if the player doesn't want to). Whichever way is the most fun for the player.

For the second question, the answer is similar to the first. As long as you play your character ICly, you're free to work with whatever physical condition the character has. If you'd rather play them free of particular conditions, you can have the wormhole remove them, but it's preferable to choose a canon point where the condition isn't present if possible.

tl;dr It's up to the player's discretion which conditions remain and which are removed as long as the player plays them ICly.