Elastic collisions with neutrinos 1: Do neutrinos undergo elastic collisions with fermions?
2: Would this imply a variable speed for neutrinos?
3: Can neutrinos transfer momenta in interactions?
 A: *

*Yes. Beam neutrino experiments regularly observe events in which a single hadron appears in the detector. Such events are attributable to $Z$ exchange reactions like $\nu + p \to \nu' + p' + \pi ${*}, or $\nu + p \to \nu' + p'$ (where $p'$ is energetic enough to register in the detector). Reactions with leptonic products are not obvious because they could also arise from $W$ exchange reaction.

*Yes. Contrary to the standard model, neutrinos are known to have mass, and thus have subluminal speeds dependent on their momentum. SuperKamiokande, SNO, KamLAND, and other experiments have conclusively shown that neutrinos mix. Work is proceeding on nailing down the full parameters of the mixing matrix.

*Yes. Indeed it is obvious in the above reaction.

{*} This event may be elastic at the level where the neutrino interacts with a parton to form on on-shell pion from the nuclear sea. Such occurrences are called "quasi-elasitc scattering" by nuclear physicists. Alas some confusion arises because neutrino physicists reserve that phase for W exchange reaction likes $\nu_l + A \to l^- + A'$.
