Your friend is Korean? If he or she is Korean, it is better to write "this year(올해)" because Koreans much more use a solar calender than lunar calender. I'm 21 in US but 22 in Korea, because I was born in 1992, and it doesn't change until the new year(2014). So it is the problem of cultural difference:) And '내' menas 'my'. In this case, you better use '너의' or '너희'. It's difficult to explain, but I would try, '나의(my) to 내(abbreviation of 'my) and '너의(your)' to '네(abbreviation of 'your')' are informal expression that are used in intimate relationship or the same age. '저의(my) to 제(abbreviation of 'my) and '당신의(your) are formal expression that are used in formal situation, talking to one's elder, or the first time to meet someone. and '이여요', Koreans almost not use that in reality. It is better to end sentence with formal expression because 'the mother of friend' is elder than you. So in conclusion, if you are close with the friend, it is better to say "올해 너희 어머니는 몇살 이시니?" or "올해 너희 어머니는 나이가 어떻게 되시니?"

The question you made, means " How old 'my' mother is 'today'? " and the correction means " How old 'your' mother is 'this year' ? " Maybe the usage for " today " does not make sense in Korean and you should use " this year " to build up a correct sentence. 내 means " my " and 네 means " your ". "너희, 너의 " I know this two also mean " your ". but I'm not sure about the difference between two endings!