At two months you can start giving your puppy RC puppy food. RC has a specialised lab food which can be given based on the age of the dog.
Just RC along with multi vitamin and calcium advised by your vet is good enough.
Do not make your puppy fat. All dogs/ puppies have a little discharge from the eye generally in the morning, like we human. The eye discharged should be cleaned with a wet cotton and then with a dry cotton. Without seeing one cannot say anything, but if the discharge is more then show to a vet. Also winter is coming so keep your pup dry and warm specially at night.