I've read that preds immune system can resist all introduced strains, meaning that it can't be poisoned, etc & that they can probably resist disease aswell, still we don't know for sure.
As for aliens well..... honestly I doubt that they can get diseases, not sure why exactly, just doesn't seem like a creature that can survive in any manner of harsh conditions could catch a disease, it just doesn't seem likely to me (btw, welcome back avier, it's good to see u again)