1) I don't think the answer comes from bond lengths and angle strain. Both the nitrogen and oxygen are sp2 so they have approximately the same angles. And I just don't feel that the small difference in bond lengths is going to have any significant influence here.
2) I think the N is more nucleophilic than you would expect. Sure an amide is less nucleophilic than an amine due to resonance. Here we have a carbamate though... so both the N and O are donating electron density into the carbonyl. I would argue therefore that the N is doing less resonance in a carbamate than it does in an amide, and thus the N is a fine nucleophile here. See Tetrahedron Letters 2001, 42, 1799 for an example of a mild N-alkylation of carbamates with alkyl halides.