>> "1)Can they change on LimeLM server for example when TurboActivate version changes (Is it possible that if I download them today and in 6 months for the same product/version they are going to be different files?)"
They're re-generated every time you download it. So, they will change 1 millisecond to the next. This is due to the nature of cryptographic signing.
>> "2)Do they change on user's computer (when activating/deactivating keys etc.)"
Never. They're read-only. TA, TF, TFS never touch the files other than to read it.
>> "The reason I am asking is that I would like to know if I can include hash of those file when verifying if user's distribution isn't corrupted."
Sure, that would work.