1. Off the top of my head I think there is a fluff excuse that all weapons have a minimum amount of articulation, torso weapons can slightly swivel and adjust(for stabilization and targeting). However, right now, I have no sources to back that up and running off my memory.
2. Yes you can mount weapons on legs, and they will always fire in the front arc, not effected by torso twisting. TT rules have rules for firing at multiple targets, in multiple arcs. So a 'mech like a
Quickdraw could engage targets in any arc as it has front, arm and rear mounted weapons. Yes, those weapons are eligible to fire, but only at a target in the respective arc. Multi-target firing is much harder and not exactly a smart thing for the average TT pilot with a skill of 4/5.
3.
Battlemechs have arcs of fire. The black spot is the hex the 'mech is standing on, we are looking down at a standing 'mech that is facing up, to the top. The red zone is the front arc, all front mounted torso(and leg) weapons can fire at targets in the red zone. Both arms can also fire to the front, but also have an expanded arc, the orange zones are the additional areas the arms can normally fire into, left arm to left orange, right to right respectively. The yellow zone is the rear arc. Real mounted torso weapons (can legs rear mount?) fire into this zone.
Torso twisting: A 'mech can rotate this chart, one hex to the left or right. This is the limit of the torso twist, if it twisted to the right, you would see the front arcs right side limit is where the right arms arc is in the image above, the right arms new right limit, is now facing behind the 'mech, as its legs are still pointing up and he has not moved.
Special Case: Arm flipping, some 'mechs that lack hand and lower arm accuators like the
Rifleman can take the arms and flip them backwards into the yellow zone. This can be done in addition to torso twisting, but a 'mech cannot flip and unflip arms in the same round.
Now that we have this base knowledge of the arcs, to answer the exact situation, you are wondering about:
Yes, if he is running forward, not torso twisted he could fire the right arm weapons to the right side, or the left arm weapons to the left side, but not both arms to the same side. The pilot could torso twist to bring both arms to bear on one side. This has been all off the top of my head and I may have gotten something wrong. Also I think I remember something about for multi-targeting the secondary targets MUST be in the front arc, which would not allow a mech to fire into both the left arm only arc and the right only arc at the same round. But I do not remember clearly enough on that. Anybody got a Total Warfare laying near by?