leadership and other rules while in a challenge

When you have a unit comprised of regular units, a character (sargeant) and Independant Character, how does getting into a challenge effect the rest of the fight.

One example is this, if you have urien, grots, and one is an aberation, and then for what ever reason (mind shackle scarabs) the aberation is in a challenge and needs to perform a leadership test, does he get to use Uriens?

Another example of my question is the vice versa, if say, the baron is in with some beasts and is challenged and he accepts, does that make it so the unit can no longer hit and run until after the challenge? also, can baron hit and run by himself and keep the beasts in combat?

Basically, does the character stop being part of the unit to accept the challenge or does he get to continue to buff the squad while in a challenge. I do believe that he still buffs the squad and the leadership test unless stating its against that specific model's leadership should get uriens.

Secondary question is, can you only challenge once per combat? I read in the rule book that "you can only challenge once per combat" so if you have a IC you don't want in combat you can just throw your sergeant in to get eaten or possibly just bog down their IC and then once dead he can't issue another challenge. I see alot of people going against this and issuing more than one challenge. Why is this?

A character in a challenge is still part of his unit for all purposes other than those directly outlined in the challenges section.

As for your secondary question, there can only be one active challenge per combat at any one time. If a challenge ends however (usually with one combatant dying), a new challenge may be issued in the subsequent Assault Phase.

The RAW seem a bit confusing on the secondary question.

The BRB, p. 64 does, as you say, state (in bold text) that "Only one challenge can be issued per close combat". A couple of paragraphs later, however, it says "no further challenges can be issued in that combat whilst the previous challenge is ongoing".

There looks to be a potential conflict here. But what the first is saying is that there can only be one challenge in each separate melee - you may have some Wyches fighting some Cultists on one side of the board, and some Incubi fighting CSMs on the other, each of these is a separate 'close combat' and there may be one (and only one) challenge in each. (This is, as it were, a spatial or geographic restriction.)

The second quoted sentence then tells you that once each combat has a challenge in place, there can be no new challenges whilst that challenge is ongoing. (This adds a temporal restriction.) It doesn't explicitly say that there can be a new challenge once the first is over, but presumably that's what we're intended to understand, since otherwise it would just say that there can be no new challenges full stop.

One area that I believe is unclear is what happens if two separate combats join into one big multiple combat. Suppose the Wyches and Incubi from my previous example weren't so far apart. Another large unit (let's say some Zombies) may multi-charge into both of them. As I understand it, this would now be a multiple combat and yet two challenges are taking place within it. I don't think the definitions of multiple combat are very clear though (perhaps the Incubi are in one combat with the CSMs and another (multiple) combat with the Zombies?)

In tha last example the challengies go on as usual but no new challenge can be issued befor both of those are solved.

To answer your firt question:
MSS work on the model in base contact its Ld. So you would never benefit from any IC Ld.
The aberration's mind is already broken by the Heamonculi and will not resist that much to being mind-controlled by anyone else.

The point about hit & Run: as the people above said, the Baron still is part of the unit, so whole the unit can hit & run. BTW: an IC can only leave a unit during movement phase.