Allylic Radicals Bromination Mechanism
The barrier to rotation in the allyl radical is low (~15-16 kcal/m) and it can undergo cis-trans isomerization.



As to question (c)(i), you're right, there are only two resonance structures.



What you show above with three resonance structures is the trimethylenemethane diradical, isobutene with 2 allylic hydrogens removed.