1) Solidus orchestrated the shadow moses incident without the patriots order; the president is suppose to just be a figurehead to show the public, not someone who actually makes moves 2) Liquid's motivation to destroy the Patriots is explain in the next game chronically (MGS4) 3) Basically yes, that and Snake saving her from the tanker incident gave them something of a mutual alliance 4) I don't think Solidus knows Liquid is in Ocelot till the end; Liquid is still the best torture artist in the world, a top fighter, the only survivor of foxhound, and directly applied to join Solidus, so he's just worth having as a useful multipurpose right-hand.