Yes it is correct. It sounds a little funny, but it is correct. It is an adverb.
Small shore as little shore is not grammatically correct
Kristin's answer to the problem was an infinitesimally small decimal.
Yes, 'for free', is grammatically correct.
"Not like that" can be grammatically correct, depending on the context.
Yes! That is grammatically correct!
No, but the difference is infinitesimally small.
It can be infinitesimally small.
This is not grammatically correct. The correct form is 'you do not know', or the abbreviated 'you don't know'.
Sure. It would also be grammatically correct to write He spoggled his nubbix on the goober. Grammatically correct and meaningful are not the same.
'What a drunkard you are' is a grammatically correct English sentence.
"That was wrong" is a grammatically correct sentence.
Yes, it is grammatically correct.