No. A model cannot shoot during the Shooting phase if it marched during the preceding Movement phase and, although they work differently to most missile weapons, Breath weapons are a type of missile weapon.

Only with those models that are on the hill. For example, if a unit consists of twenty models in two ranks of 10 and only 5 models in each rank are on the hill, only those 10 models can claim the benefits of shooting from a hill.

A unit that is closer to the top of a hill (i.e., the centre of the hill or the edge of the battlefield) can draw a line of sight across and shoot over one that is closer to the bottom. Units cannot draw a line of sight across or shoot over units that are closer to the top of a hill than they are.

Missile weapons mounted on chariots (or howdahs) are shot by the crew, using their Ballistic Skill.

As many as they know. Though there are exceptions (some magic items allow a Wizard to know extra spells but limit how many they can cast per turn, for example), a Wizard can usually attempt to cast each of their spells once per turn.