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.

If a model is able to fight, it must make all of its attacks.

Yes. Unless they have been killed, models that are in a fighting rank or that are 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(s) that are able to fight (starting with the first fighting rank) and, secondly, the number of models in the 'supporting rank' that are able to fight.

Yes. As stated on page 150, models cannot fight during a phase in which they stepped forward into a fighting rank. However, models already in a fighting rank can step forward and close in as described, maximising their number of Attacks.

If a unit has and is able to use the Press of Battle rule, it can do so regardless of which of its arcs the enemy is engaged with.

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. Whilst a charging unit will become disordered, and whilst Impact Hits and Stomp Attacks cannot be made due to the presence of the obstacle (as stated above), units are otherwise able to fight normally across a low linear obstacle, as if they were in base contact.

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.

As stated on page 123, units must move forwards unless performing a manoeuvre (or when Giving Ground). This includes whilst pursuing.

No. As stated on page 125, units ignore other units whilst pivoting.

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.

Exactly what it says – the pursuing unit counts as having charged its enemy during the next turn of the game, when the combat is fought, even though the unit will not actually have moved during that turn. This means rules and weapons that can only be used by charging models can be used, that Initiative modifiers for charging are granted (based on the distance the unit pursued), and so forth.