Questions using ‘Why’ and ‘How come’ have different forms and are used differently. With the verb form ‘be’ (i.e. is, am, are, was, were), when used with ‘how come’ there is no inversion of the noun and the verb and the structure is maintained like a sentence (noun-verb form).
How come she is at the party?
How come she was at the party?
How come they are angry?
How come she is writing the letter?
When ‘be’ is used with ‘why’, there is inversion of the noun and the verb.
Why is she at the party?
Why was she at the party?
Why are they angry?
Why is she writing the letter?
If the verb is a form of ‘have’ or another verb (i.e. write, talk), the form also changes. With ‘how come’ the form is like the above, with no inversion.
How come she went?
How come she has to go?
With ‘why’, an insertion of a form of ‘do’ before the noun is required.
Why did she go?
Why does she have to go?
As for usage, although both ‘why’ and ‘how come’ is eliciting a reason, they are used in different situations. A speaker would use ‘how come’ if what he/she thinks is not the situation.
How come she is at the party? (I thought she wasn’t going to come.)
A speaker would use ‘why’ if he/she wants to know the reason but does not have a presupposition.
Why is she at the party? (I want to know the reason.)