Of course, unless your brother has some sort of incestuous history, but I am assuming he does not or else you would not even ask this question.
There is no actual blood relationship. In most instances you call them the brother of your daughter in-law. Or just introduce them by name and let people guess if there is a connection.
It depends on the age of your daughter and the maturity level.
Age 11.
I let my daughter wear thongs because I think that there is no major difference between normal panties and thongs.
at least 16
IF she needs one. Otherwise, no.
no
This depends on wether you trust your brother not to break or tear it up.
yes if she would like to go then let her and you should probably go with her
No.
maybe you should just let her know how you feel
If I knew the parents and trusted them to care for my child as well as I would, then, yes, I would. But an exception to this would be if my daughter was a teen, and they had a teen son who was going on the trip, too. In that case I would not let her go.