Well, yes.
1) It's in Google's hands. So, they can read what you type. Don't like that? Then don't use it.
2) They will store the documents very well (they're pretty good at this), but you'll find in the small print that if there is a catastrophic error and everything is lost, then it's not their fault.
3) Obviously, without an internet connection, you'll have no documents.
Personally, I'd advise you to stick with using Word or whatever. It's more reliable, and definitely more secure with regard to your privacy.