Tradeoff between Filter Order and Sections
Large order single stage filters are inherently problematic. Calculating the numerators and denominator from the poles and zeros is an ill defined problem and numerically unstable. 
Furthermore Direct Form II is the worst possible filter topology. I strongly recommend Direct Form I or transposed Form II.

To the questions:


Numerically ill defined problem
Just add the group delay of the indivdiual stages
Group delay is always defined as the negative first derivative of the phase of the transfer function vs. frequency. That's the same for FIR and IIR. It's frequency dependent.
Yes. If you had infinite precision math, the results would be the same.
Very important. You can't implement and unstable filter, you'd only get noise NaN or infinity as output
No idea
Pretty much everyone implements filter ins biquad sections. So the number of stages and the filter order is directly proportional