Is it safe the leftovers in freezer are not frozen yet

A lot of dairy products become watery or start to separate if they've been frozen or defrosted: pastries with cream fillings, cream cheese, sour cream.

The USDA says does not recommend that eggs or canned foods be stored frozen. Eggshells can crack easily, and even if the shells remain intact, the consistency of egg yolks makes them difficult to use for anything other than hard-boiling. Canned foods that are frozen accidentally could pose health risks, so the USDA recommends inspecting to see if the can has rusted or burst. If the can is swollen, thaw it but check to make sure it doesn't look or smell off before eating.

The FDA also has a useful chart (pdf) on which foods don't freeze well and how long you can freeze other foods. (Note: when there is a recommended limit on how long a food should be frozen, it indicates when the quality of the food will decrease - NOT when it will "expire". You could theoretically freeze most foods indefinitely.)

The only other thing I would avoid freezing is any sort of raw green (lettuce, spinach, etc.). Greens wilt and turn brown when you freeze them. (If they're cooked, they should be fine to freeze and thaw.)

EDIT: Apparently, some spices become bitter when frozen, including pepper, cloves, garlic, green pepper, imitation vanilla, and onions, paprika and celery taste different.

I freeze cheese all the time, mostly mozzarella. It keeps longer. (If I keep mozzarella or similar cheeses too long in the fridge it gets moldy, often even before its expiration date.) However, I usually use frozen cheese only for cooking - i.e. if it's going to be melted. Freezing cheese does change the texture. Parmesan, though, being a hard, aged cheese would probably be less affected by freezing. However, on the same token, aged cheeses keep very nicely in the fridge, so I wouldn't see much benefit in freezing it.