No you cant
No you cannot.
You can't stay overnight but you can be the temple till about 8 or 8:30 p.m. Is that what you are looking for
I don't think they let you stay overnight. But i am sure there are places close by that provide accomodation. You might want to call the temple and check
No not in Bapa Swaminarayan Mandir but you can go to Vraj Temple in Philadelphia they have arrangements to to stay there
No
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