Can a family member give a kidney to a person in need of a transplant?

Yes. In order to donate a kidney, the donor and recipient must be a match. Family members are often the first choice when it come to kidney donation, because they have the highest likelihood of being similar genetically. There are times though that even family members are not a good match ( a poor match increases the chance that a donate kidney will not work). In that case other people may be checked.
Yes. Yes but the donor and recipient still must be tested to see if a match occurs. Family members as donors can improve the chances of a match, but do not guarantee a match.