Yes they can be friends. It is hard when one of you has feelings for the other that is "more than" friendship but I have seen even this can work. It is not for everyone. Ask yourself if you would be comfortable talking with her about her new boyfriend? Will you be happy for her? Would such a conversation bring you down so low that you are wallowing in it after she goes home? If the answer is yes then you cannot handle being friends with her. If you believe you can be supportive of her in a new relationship (like any friend would) then you can certainly give it a shot. You will know if your feelings for her are getting in the way of the friendship. If that happens you will have to end the close relationship you two have. Perhaps keep in touch via text and not see each other. Or see each other rarely.

If you stay friends, I would not recommend that you rent your room out to her. This is inviting the end of your relationship for sure. I don't see how you could tolerate if she brings guys back to her room. Better to keep her at a safe distance where you are forced to make time for each other and not take it for granted that the other one will be there because you're living in the same house.