I'm not aware of He3 easily becoming T. I know T spontaneously becomes He3 (emitting a positron and a neutrino) with some probability, a very low one, not relevant at the scale of a pulse
Yes, and that's not a problem either here, because the neutrons don't stick around. If you had a lithium blanket making T you'd want to clear out any 3He as it was produced from T decay so they don't hoover up too many thermalized neutrons, though.
I don't think that (n,p) reaction on 3He normally produces a photon, btw.
Instead, a neutron strikes ³He producing T, H and a photon.