Ammo explosion: You take the remaining ammo (let's call it 6 shots) and multiply it by the amount of damage the weapon can do MAXIMUM per shot. For an LRM 10, that is 10. SO we multiply 6x10, and get 60. This damage occurs in the location where the ammo suffered the critical hit, then transfers inward towards the center torso just like other damage, except the ammo explosion ignores armor, and only goes through internals.
So for our example, let's say he has 10 internal structure left in the left torso, where the ammo suffered the critical hit. You have suffered 60 (ouch) points of damage.
10 damage of that destroys the rest of the left torso internal structure. 50 damage from the explosion remaining.
The damage transfers inward towards the center torso. It ignores armor and goes straight through internals. This is why most ammo explosions are pretty fatal to introductory 'Mechs.
The Dragon has 20 internal structure points in the Center torso. It suffers 20 damage and destroys the 'Mech through center torso destruction with 30 damage remaining that is lost in a pretty light show. 'Mech is super dead.
Piloting Checks:
Yes, your base number is your piloting skill number. No matter what you did on the turn, if something happens that requires a piloting check unless you are already on the ground.
All of the modifiers are cumulative for your rolls. You also have to make a roll for EACH thing which causes a piloting check.
In ONE PHASE (weapon attacks OR Physical attack phase)
Your 'Mech takes 20 points of damage for a +1 penalty.
You have a broken lower leg actuator for a +1 penalty.
And your gyro has taken a critical hit for a +3 penalty.
If your piloting skill is 5, your total piloting skill check to remain standing is an 10. 5+1+1+3=10.
The part that sucks is that you have to make THREE checks at a 10+ to stay standing. Each penalty causes a separate roll, with the modifiers for all effects.
Once the Physical attack phase comes around the modifiers all apply again, with the 20+ damage modifier "resetting" every phase. So if you take 25 points of weapon damage in the weapon attack phase, but only 10 damage in the physical attack phase, you do not apply the +1 for 20+ points of damage.
NOTE: These modifiers only apply if you are doing something that requires a piloting skill check. Let's say you have that damaged actuator and gyro crit, but only suffer 15 points of damage in the weapon attack phase, you do not require ANY piloting skill checks, because nothing has caused you to make a piloting skill check.
Gamer's Note: I know a LOT of groups do not play with the standard rules. In my group, we only make 1 roll with all the penalties per phase. Otherwise some games turn in to DominoTech, with nothing but 'Mechs falling over everywhere, and that's not fun.