Is there a name for a statement someone makes, in which they issue a command for feedback, or request information, but the answer they want is totally obvious?
For example, your friend shows you pictures of his backyard pool, drinks, and girls who hang out with him, and says "so let me know if you're coming over this weekend".
It's similar to a rhetorical question, where the asker knows the answer and is essentially asking himself. What would this case be called?
The Chicago Manual of Style, Fifteenth Edition (2003) terms requests or instructions of the type you seem to be talking about "courtesy questions" and considers them to be so unlike normal questions that it says they don't require question marks:
6.74 Courtesy question. A request courteously disguised as a question does not require a question mark.
[Example:] Would you kindly respond by March 1.
[Example:] Will the audience please rise.
You can call it a "foregone conclusion" that the invitee will attend - especially after seeing what is in store for the weekend!
n.
1) An end or a result regarded as inevitable: The victory was a foregone conclusion.
2) A conclusion formed in advance of argument or consideration
Perhaps a given
something given; especially : something taken for granted
Or a sure thing
one that is certain to succeed : a sure bet
