The adjective is chosen according to gender. It's en fråga, so we get this form. For ett nouns, the adjective gets the -t ending. Ett viktigt svar is 'an important answer'.
So it's en viktig man but also en viktig dag because both of these are en words.
I would say no. They have similar roots and evolved together. If it is a loanword it would ve come into the language much later.
It is a germanice language, like other scandinavian languages and dutch german and english. So there will be many similarities