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.

Yes, provided it has a Unit Strength of 5 or more (as per the errata on page 1). As mentioned previously, a Close Order unit of just one model is still a Close Order unit.

No. Even though the units separated momentarily, they remain locked in place and engaged in an ongoing combat once the Follow Up or Pursuit move has been made. In other words, because the combat is ongoing, neither unit is able to swap one weapon for another.

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.