Learn English – Simple present vs. present continuous

The distinctions between these phrases may be somewhat colloquial and/or what I'll call "teen-speak" but at least in the US they tend to be used for decidedly different purposes and are not interchangeable in those contexts.

"To my face" is used to mean "in my presence" For example someone could say:

She'll say that when I'm not around, I'd like to hear her say that to my face!
(...say that while we're looking each other in the eye)

"In my face" is used when someone is confronting you, arguing with you, or pointing out that they believe you have done something wrong.

I can't believe my mom "got all in my face" just because I forgot to take out the trash
(...my mom was yelling at me [perhaps even with her face just inches from mine])

The baseball team manager was so upset by the umpire's call that he got right in his face and was yelling at the top of his lungs.
(...the manager was literally nose to nose with the ump telling him exactly what he thought of the call)

at my face has no special connotations

He pointed a gun at my face - probably means the bullet would hit my face if it were fired, while if the gun barrel were just a few inches from my face, I'd be more likely to say, "*He had his gun in my face"

So having said all that, the first two of your sentences might likely be heard from a native speaker in the right situation.
The third statement would probably never be.

They mean essentially the same thing: Are you going home this summer? which is probably the most neutral form of this question.

However Will you go home this summer? might be seen as being curt and could imply that you wish for that person to leave. It could essentially be taken as Will you please go home this summer? but without the please.

Will you be going home this summer? is more inquisitive. It implies that you are merely curious about to their summer plans and you don't particularly care what the answer is.

If this is being addressed to a person that you do not wish to go home for summer you could try asking You aren't going home for summer, are you? which retains the overall neutral value but implies that you prefer for them not to leave.