Question a - no
Whats to burn? There aren't even any possible overheated tyres/brakes in the holes, just a large draft cooling everything off.
Question b - no
On most runways you will be in desperate trouble trying to RTO without antiskid. Do you have HMGs and/or RAT on B737? That ought to enable you to get airborne and sort it out. What else would you lose with no AC power? eg Would the spoilers still work?