If "close" is code for you find them showering together or dressing each other in lingerie you might be suspicious that there is a part of their lives you were not aware of - and should ask.
If by "close" you mean they like to hang out together, consider that your brother may share personality traits with you (interests, humour, music) that your husband would look for in a friend as well as a spouse. In many families relatives and in-laws form very close knit relationships and communities because of common interests and compatible personalities.
My wifes brother in law!
If you have evidence or reason to be suspicious of something, then keep a close eye on him. It is hard to give a good answer unless I know what you are suspicious of. If you are just suspicious without evidence, then you need to trust him. Get counceling if you need to. I have seen 1 marraige fall apart simply because the husband never trusted the wife.
Discuss it with your husband to decide if brother should be asked to leave; or if you are somewhere other than your home, if you and your husband should leave. No one has the right to interfere with your relationship with your husband (other than an abusive situation).
Yes, for a nephew is sister's son, brother's son, wife's brother's son, wife's sister's son, husband's brother's son, husband's sister's son
Yes
If you got pregnant with you ex and then married his brother, then you kid will should call your husband dad even though he is no the real father.
It shouldn't matter if he likes your husband, what really matters is that you love him. Your brother should focus on his own life, and let you get on with yours.
his name or brother-in-law
I think it is appropriate to call him your brother.
I really don't know but no one should marry their brother it is gross!
You can refer to her as your sister-in-law; in person you should call her by her name.
Your husband's Brother would be your Brother-in-law. Some people feel that his wife would be your Sister-in-law, other people feel his wife should be called "My Brother-in-law's Wife". I prefer to call her my Sister-in-law. Perhaps you could ask her what she'd prefer to be called.