Can a Gentile still be in God's house?

Answer 1

yes. God's house is church. God saves all people, including Gentiles. Jesus came down to die on the cross in order to give all people to opportunity to accept Him as their Saviour. And even if you have not done that (which you need to) there's nothing that's going to stop you from walking into a church building.

Matthew 28: 19-20 : These twelve Jesus sent forth, and commanded them, saying, Go not into the way of the Gentiles, and into any city of the Samaritans enter ye not: But go rather to the lost sheep of the house of Israel. Matthews 10:5-6 Matthews 15:22 And, behold, a woman of Canaan came out of the same coasts, and cried unto him, saying, Have mercy on me, O Lord, thou son of David; my daughter is grievously vexed with a devil. 15:23 But he answered her not a word. And his disciples came and besought him, saying, Send her away; for she crieth after us. 15:24 But he answered and said, I am not sent but unto the lost sheep of the house of Israel.