1. A group of middle school students who help small children.

2. A group of middle school students who helps small children.

(Do we have to use 'help' or 'helps'?)

3. World War II
1) World War Two
the Second World War

2) World War two.
the second World War

(Which one is correct, 1) or 2)? Do we have to capitalize 'two'?)

Neither # 1 nor 2 are complete sentences. However, the subject is "group"... this is singular so the verb would singular also.

In #3, the first one would be correct.