A non Muslim can enter a mosque, but should remove his shoes
as Synagogue is to Jew
No. Jewish custom is never to enter the house of worship for another religion.
Yes.
no
It is halaal, there is nothing wrong with drawing a mosque or building.
no
they must remove there shoes.
Yes.
yes
in lots of Islamic country women are allowed to enter mosques , but not along with men , because the main goal of going to mosques is worship and it needs a pure desire to consent rate in ALLAH , as the host of the house of praying , however due to the nature of desires between strange men and women , sometimes it could bring some other thing between them , then it would take from them the interest towards the pray, to do so they have brought separate areas for women and men in the mosques, like putting a curtain between them and it is usually occurs in my country .
i dont think its allowed.