Hello. Sorry you haven't had any replies yet! Usually when you first get a hamster it's best to give veg every 2 or 3 days until their stomachs get used to it. Too much too soon could possibly give them diarrhoea. Within a couple of weeks, when you have gone from every 3 days to every other, day, and they are fine, you should be able to give some every day. Just a very small piece about 1cm cubed size (doesn't have to be square - that's just an idea of size). There are many safe veg and some unsafe ones. I tend to give one out of broccoli, carrot, cauliflower, green beans, sugar snap peas, baby corn - and try and give a different one each day, so not the same one every day. Unsafe ones are onion, garlic and tomato. There are others, but I just stick to safe ones
Lettuce and cabbage aren't generally recommended. A tiny little piece occasionally should be ok but I prefer to stick to the others that aren't a problem.
It can be raw or cooked as long as the cooked is just plain boiled. Raw is better really, but if you've cooked some carrots or broccoli for tea then saving a bit for the hammy can be good!
If you've been giving it every day and your hammy is fine then it should be fine to keep giving a bit every day. They love fresh food and love veg usually and it's good for them. Needs to be washed first obviously!