He was probably feather picking from the stress of losing his mate but it could also be a medical reason so having your vet check both of them would be a good idea. In the future, when getting a new pet, make sure you quarantine them for at least 2 weeks prior to introducing them to your pets. This will prevent them giving you healthly pets something...of visa versa. As far the egg thing, I would remove the eggs because more than likely they aren't fertile unless you have seen them breeding. Watch her closely and if she starts acting depressed or goes off food and hasn't layed an egg, she could be eggbound and would need to be seen by a vet.
Let me know if you have any other questions
Good Luck &
Best Fishes