Translation:Can I go home?
I used "Can I go home?" and it was accepted. Technically, both the first person singular that we used and the first person plural that Duolingo used are both correct, as pronouns in Japanese are determined based off of context, and there is none in this situation. Furthermore, "can I..." and "is it okay for me to..." are literally the exact same thing, just different ways of phrasing. I believe this is just Duolingo being overly-picky. So yes, both "if I" and "if we" are correct, if there is no context to state otherwise.
This comes up a lot in the comments section. If there is no context, assume it is about oneself and therefore use "I". It will never be marked wrong.
Also, "is it okay..." and "can I..." are not literally the exact same thing. "is it okay..." is a little politer/softer sounding. But, yes, they do both mean the same thing.
"帰る" reminds me "go back where you belong". So "家" is natural place where you go back. But occasionally it may be a hometown (帰郷), country(帰国), or the earth(帰還). ... In those cases you cannot omit them.
If you add "家に" into your sentence, it makes clear where you go back. It makes sense without "家に", if you go back to home.
Not unusual if the person is asking/needed permission to leave eg. a student asking if it's alright for them to go home yet/confirming if it was home time yet or if the teacher was letting them leave early. Or if people had been evacuated from their homes and they wanted to check if it was safe to return home. Or if school or work had closed early perhaps due to severe weather conditions and students/employees were confirming that it was ok for them to return home early. Or for children in after school care of some kind inquiring whether they could return home yet who need to wait to go home till someone of a legal age to care from them is home. You also might ask this if your home or building was being fumigated or had a gas leak. Plenty of situations for which this sentence makes perfect sense.