Yes-no questions in English usually start with a verb, either a form of "do" or the main verb.
So "Can we go to my house?" would be a question - but not a translation of this sentence, since "hejmo" (home) is not "domo" (house).
Your sentence is more of a suggestion, and I wouldn't expect a "yes" or "no" answer to it ("OK" would be more likely, i.e. "I accept your proposal"). In Esperanto, I wouldn't render it with a "ĉu" sentence (which makes yes-no questions) but with something like "Ni povas iri al mia domo?" - i.e. a regular statement, as in English, but with question intonation.
But you wouldn't say "let's go to my home" in English. If they don't live there, you say "let's go to my house." What you say to your mother or your roommates or spouse is "I'm bringing someone home." If you're out of the house (not 'home"!) with a group of friends and say "let's go home" or "let's all go home" you generally mean to your respective houses -- you're not suggesting they all come home with you. To invite them home with you, you'd say "let's go to my house" or "you all come to my house." Does Esperanto not make this distinction?
I hate the lack "edit" here. Anyway, i agree with you about "my house" and in English it is common to omit a word like can instead using tone to indicate a question. The sentence here seems to be asking if it is possible to go to your house rather than propose doing so.
-n is added after prepositions only for the small set of prepositions that can indicate either a position or a motion.
"al" always indicates motion/direction and so it never takes -n.
Similarly with "ĝis" (up to) and "laŭ" (in its spatial meaning "along") which also always indicate motion and never take -n.
I made a mistake in my typing and "How about we go to my home?" shows up as the correct solution. Surely that isn't anywhere near being correct? Also, apart from English being ridiculously ambiguous and confusing people, how come Esperanto mixes up expressions of ability with requests and wishes?
At least if this course is anything to go by, it just seems to mimic the inconsistencies of English in what are accepted translations of povi, which I thought was supposed to only mean "can" in the sense "be able to"