what if/past

A: What time is it?
B: It’s a quarter to 12. Why?
A: At noon, on the dot, I’m supposed to meet James.
B: On the dot? What if you don’t get there until a few minutes past four? Will you turn into a pumpkin?

I would like to know the meaning of “what if” and “a few minutes past four”.

I can’t see what could be a problem with “what” and “until a few minutes past four?”.(Should “what happens if you don’t get…” be there?)
On the other hand, I am interested in the last question from the dialog,‘Will you turn into a pumpkin?’
Why did he, at length, asked that question?


P.M. on dot ~ exactly on time

“What if” is used in the beginning of the sentence to suggest that there will be some consequence (either negative or positive) to the action that follows the “what if.” Another way to read your sentence is “What will happen if I don’t get there until a few minutes past four?”

“A few minutes past four” indicates a time somewhere between 4:01 and 4:10 (not necessarily stopping at 10).

“What if” is just fine without inserting “happens.” However, it is fine with it as well.

The question at the end “Will you turn into a pumpkin?” is sarcasm. Person B is mocking James’ demands that Person A be there at exactly noon.
Another way to phrase that sentence is “On the dot? What will James do if you don’t get there at that time, turn you into a pumpkin?”

To add to this:

In the fairy story, Cinderella was told by her Fairy Godmother that she had to return home by midnight, as on exactly the stroke of midnight the spells she had woven would be broken - Cinderella would once again be poor and in rags - and her coach would turn back into a pumpkin.

This is the origin of the phrase.