A choccy drop is ok for a treat but not too often and anyway she will enjoy them more if she has them few and far between
The diabetes is less common in syrians but can still happen, so if its avoidable its best to do so
Yes cooked egg (dont want her to get salmonella lol), scrambled or as a mini omlette is nice you could even make her a spinach/carrot omlette lol
She is a very lucky ham to have a mummy/daddy like you to care so much.
If you are intrested there is a list of Hammie suitable food on the wiki to help: heres the links:
safe and unsafe foods:
Safe and Unsafe Food and Plants - Hamster Central WIKI
common fresh foods:
Common fresh foods for your hamster - Hamster Central WIKI
Hope this helps