Miles/Segments for Divert
 

One quick question about being diverted to an alternate airport, say for fuel, does this count as an additional segment for mileage/elite qualification purposes?

Would it be different if it was the last flight of the day and you had to stay overnight?

Nope.

As for the overnight: ? My guess (complete guess) would be that if the next day's flight was a different flight number and you were issued a new boarding pass with said flight number, you might have a shot.