In short, I would look in the manual every time.
It's not necessarily just for the Square Root. For the Cosine, it would be "COS(" or [Ctrl]-[C]. Since many functions would use a similiar format, you shouldn't need to look at the help more than once. Then it depends wheather you like to press [Ctrl] or not.
No, not yours. Unless you build in a scientific feature with the n! function.
Mine has that. It can return 200! (although it is not fully accurate with such large numbers). But if you type 999999999999! it won't freeze!!
The variable that loops to solve this recursively is a 16-bit integer, so it at most loops to about 32,000. It can do that in less than a second, and just exits the loop with an error. It works and I hadn't even thought about that.
And I have no idea what the function is for SQRT (although ^.5 would probably do it).
QBasic has a fast built-in Square Root function, which is one reason I think my calculator should.