Shooting at a Mixed Unit

Let's say there are 6 models in a unit left...

1 champion, 1 hero,1 Lord and 3 regulars...

I hit with 6 shots, how can I distribute them?

Now you seem to be talking about the six smaller repeating bolts, which follow the normal rules of Shooting, and not the rules of a Bolt Thrower shot.

Regarding Q1:
Since there are less than five rank-and-file models, you randomise, although in this particular case it means that every model is hit once, because "the controlling player [...] must allocate one hit on each model before he can add a second hit on a model" (BRB p. 99).

Note, however, that a "champion cannot normally be targeted by enemy shooting attacks — he can only be removed as a casualty if there are no other rank-and-file members of his unit left (not even the standard bearer or musician)" (BRB p. 93). So, you need to resolve the hits against the regulars first, and then resolve the hit against the champion on any survivor (if there is one).

Regarding Q2:
No, because he does not have the same troop type (Monstrous Cavalry versus Cavalry).

BRB p. 99: "If there are fewer than five rank-and-file models left in the unit (or the character is of a different troop type) there is a chance that any characters in the unit could be hit — the controlling player decides who is hit, but must allocate one hit on each model before he can add a second hit on a model; he must allocate two hits on each model before he can allocate a third, and so on."

The allocation is 1 hit per model, before any model receives an additional hit. If there are more hits than models, you can choose which models gets hit a second time, as long as all models have received one hit first - and so on. So, the first option is the correct one.

Note that you can use the allocation of hits not just to protect characters, but also rank & file models. If the character has high WS & AS, you can purposely allocate one hit to the character, thus saving one R&F model that would otherwise likely die.

It is the player that controls the unit, to wit (e.g.):

BRB p. 18: Each target unit must declare and resolve its own charge reaction (in the order chosen by their controlling player).

BRB p. 23: On occasion, exceptional dice rolls from charging units might mean that more units can complete the charge than can fit in base contact with the target. When this happens, the controlling player of the charging units must nominate which units complete the charge.

BRB p. 24: A unit that has successfully rallied immediately makes a reform manoeuvre, as described on page 14, so that the controlling player can at least get his troops pointed towards the enemy again, rather than the wild blue yonder.