What are the favourite foods of mice, and are you allowed to give them a bath?
Mice are scavengers, and so will really eat more or less anything. Going from the more gruesome details on the internet of what best to use to catch them in traps, it seems that mice like peanut butter and chocolate. Though a website which knows better says the following:
In the summer they love the yellow Dandelion heads, and also seeding grass, but don't overdo this. They also nibble a little carrot and mice are also partial to boiled rice (remains of the Chinese takeaway) and pasta. Mice are basically omnivorous, but it is a myth that they love cheese. It doesn't do them any good and is only used in mousetraps because it smells strongly and has a good texture for putting on the little spike.
If you're feeding a pet mouse, pet websites also seem to recommend various seed mixes which you could buy from a pet shop.
As for washing, this other website (both are linked below) says:
If your pet smells, it is an indication that the cage is not being cleaned often enough. You may give your rat an occasional bath (especially the males as some tend to get a yellow skin on the back and have more of an oily coat). Both rats and mice will wash themselves like cats do and you will see them constantly grooming themselves and each other. They’re also clean in their housekeeping, usually urinating in one corner of the cage. Female mice are preferred by many because they do not have the “musky” odor that is natural for male mice.