A character can be picked out if they are the closest 'target'. Target means a unit that the shooting models are allowed to shoot at, and so would not normally include units in combat, and certainly doesn't include units that are out of line of sight. Of course, this can make things difficult for Skaven, but that's what happens when you give a rat a machine-gun.

Yes they can.

In general the rules for which base size a model has is simple - the one that it comes with! Yes, some difficulty arises because over the years monsters have been mounted on a variety of base sizes. As we go through the Armies books and miniatures range, all monsters will eventually be packaged with 40mm or 50mm bases. Any mount with more than 1 Wound is a monster (or a larger than man-sized single model such as a Doombull) and is treated as being larger than cavalry for the purposes of targeting. Anything that is a 'large target' is bigger than anything else, including other monsters. If you have monsters on cavalry bases to fit with your units, we suggest you mount them on 50mm bases (like Daemonic Mounts and Tyrion's Malhandir). This helps the unit rank up more easily. If they are normally fielded as independent models, such as a Pegasus, a 40mm base is fine. Except for the fact that a 50mm base will contact more models in combat, models on 40mm and 50mm bases are treated as the same size unless they are a large target.

Yes. Both base sizes are used for characters considered to be roughly man sized and on foot and are treated as the same size for purposes of targeting.

Yes. A character in close proximity to a rank and file unit of 5+ models can only be singled out if he is larger. Note that the only current specific exemptions to the "proximity" rule discuss a larger model.

He is protected. There are no rules that state that the rank and file models providing the "protection" can't be larger.

Yes. In Warhammer, the targeting and the removal of casualties is done on a unit basis rather than on an individual model basis as in other game systems. This means that as long as one model in a target unit is within range of the firing/casting models, then the entire target unit is subject to being killed. Note however that it is the owning player who removes casualties from his units. Casualties are removed from the back ranks of ranked units, and as the owning player wishes in regards to skirmishing units. This means that the owning player may remove casualties from the back of skirmishing units in order to preserve those models that are closest to the enemy.

Simply apply a -1 modifier to each of the shots. No specific mention or example of the penalty being cumulative exists.

No, you can't target an enemy unit engaged in hand-to-hand combat (except for special rules like Skaven).

Yes.

Yes, 6" is correct.

No. They don't really follow any of the rules of skirmishers, they merely ignore terrain while they are running frantically (and randomly)!

A bolt thrower shooting at a fleeing unit will only ever hit one model.

No. Skirmishers do not form into ranks outside of close combat and thus the maximum amount of models that can be hit by a Bolt Thrower is one. Note that a skirmish unit is required to adopt the loose skirmish formation as soon as combat ends.

No. Having part of your unit out of cover is like being a little bit pregnant. Either you're completely in cover or you're not. If the unit shooting has line of sight to any models that aren't in cover, the unit being shot at can be targeted without the cover penalty. The same answer would apply if the situation involved a ranked unit with the front rank outside of the woods and the remainder of the unit inside of the woods.

In general, the normal rules for shooting apply. If there is a unit which can be reached by the shooting attack with the shortest range, the model cannot Divide Shots. Otherwise (i.e., no unit can be reached by both shooting attacks) the Divide Shots rule applies and the shooting attacks can choose different targets. Note that if the only target within range of the breath weapon and the missile weapon is a single model, the Divide Shots rule also applies and the shooting attacks can choose different targets.