Are these questions grammatically correct?

These questions are grammatically correct. In written English, there is nothing wrong with indicating an interrogative solely by putting a question mark at the end. In spoken English, intonation is used for this purpose. There is no requirement that the interrogative mood be clearly expressed in the words used.

You can certainly start a question with "you" or "that". The easiest way is by eliding a word like "do", "did", "are", "is", or "can":

Omitting "do": You really expect to make out in that sardine can?
Omitting "did/does": That help?
Omitting "is": That what you were looking for?
Omitting "are": You sure?