Continuing to Explore Four Consecutive Numbers

This problem follows on from, Starting to Explore Four Consecutive Numbers.

Take four consecutive numbers, $a$, $b$, $c$, $d$.

1. Why can't $bd-ac$ be even?
    
2. What is $bc-ad$ always equal to?
    
3. Why must the sum $a+b+c+d$ have an odd factor?
    
4. Why can't the sum $a+b+c+d$ be a multiple of $4$?
    
5. Which consecutive numbers are such that $a+b+c+d$ divides exactly by $3$?

If you enjoyed working on this problem, you may now want to take a look at the follow-up problem, Is There More to Discover About Four Consecutive Numbers?. 


With thanks to Don Steward, whose ideas formed the basis of this problem.