I couldn't find a direct explanation for these questions in the PHB:
Is it possible to wield two-handed weapons, a shield or dual wield whilst mounted?
Is it possible for a rogue to dash in, attack, then use a cunning action to disengage while mounted?
Does your mount become the target of an enemy attack against you while you are mounted?
Is it possible for a monster to choose whether to attack the PC or the mount in combat?