Slitherine

Can a unit fire support from a building?? (if building in support area)

Can a unit provide rear or flank support from a building ? My guess NO?

Can you assault from a building? I think not but cant find anything stopping you in the rules.

Can you pursue into a building? Do you need a CMT enter if so?
my guess yes/yes?

Check the downloads section for full building rules that are updated.
If memory serves me you can not assault from a building, nor give support.
Only way you can pursue into a building is if your target was defending the building and you broke them and they had to retreat, then you can move the assaulting unit in.

SO a unit losses combat (just in front of a building) making retire move into the building (occupying it cant defend) the winner unit if it makes a pursuit move cannot enter the building?

Only one unit can ever be placed inside a building terrain piece. Pursuer would end pursuit in contact with the terrain piece, next round you fight again.
If memory serves correct only way you can move into a building from pursuit is if you assaulted a building and routed the defenders.

If you pursue and end touching a building that the enemy retires into, you fight them a gain next turn - with both sides counting as if in rough terrain.
I had this at the weekend. The attacking unit fought at 1 cohesion level lower, as did my unit 'occupying' the building. Sadly my unit, having passed its test to receive a charge while wavering, then had no dice in combat ... and was subsequently routed.