When the model's turn to fight comes.

Models not engaged in a challenge cannot direct their attacks against models that are. In other words, any models that would normally have to direct their attacks against the character are free to direct them instead against the other unit their unit is engaged with.

Yes, if they have not been killed, models able to make supporting attacks can do so as normal. In other words, casualties inflicted reduce firstly the number of models in the fighting rank that are able to fight and secondly the number of models in the 'supporting rank' that are able to fight.

A model with a split profile consists of not one model, but several, all sharing the same base. Therefore, each model on that base could make a single attack. In the case of a cavalry model, for example, this would be one attack from the rider and one from their mount.

No. Models must be in base contact with the enemy to make Impact Hits or Stomp Attacks.

Yes, provided it has a high enough Unit Strength (as per the errata on page 1). A unit of just one model is still a unit.

Should any part of a unit cross beyond the edge of the battlefield whilst it is Giving Ground, the entire unit is removed from play and counts as having been destroyed.

The unit's movement stops immediately, as if it were surrounded.

It may happen that it is simply impossible for a pursuing or overrunning unit to move without it ending up 'on top' of another unit. In such cases, the unit does not move, but is considered to have made a pursuit or overrun move.

Unless it pursued into a fresh enemy, yes. A unit that overruns makes a normal pursuit move and, since its enemy has already been wiped out, it may attempt to reform as if it had run down its foe, as described on page 129.