If you have 33 students, the mean of whose ages is 13 and you remove three students, one 18, one 17 and one 5 years old, you use the average formula.

The sum of the terms divided by the number of terms = the average.
In the original case we do not know the sum, so we will use S. Our formula becomes
S/13 = 33. That tells us that S = 429.
We then subtract students age 17, 18 and 5 = total 40 years. Our new sum is 389 years, but we now have only 30 students so our new average is 389/30 = 12.967 years.

I am not sure I understand your second question.