What? I couldn't follow that at all.
By RMSR, you get -15 for not training in the weapon in that hand. So, learn dagger in left hand, rapier in right hand. You are right-handed. Fight with the dagger in the left hand, suffer a -20 "off-hand" penalty. Fight with the dagger in the right hand, fight with -15 for weapon skill bonus. Fight with the rapier in the left hand, suffer a -20 "off-hand" penalty, weapon skill bonus is -15.
Now fight with both of them together. You now use TWC. Unless you actually have developed TWC, you have a skill bonus of -30 and only Profession and stat bonuses from category. The -20 does not apply, since it appears on p. 96 under the "One-Handed Weapons", but not under "Two One-handed Weapons". There is a -20 for switching hands with your two-weapon combination under the skill description (where it gets labeled "Two-Weapon Fighting", minor oops) on p. 162. So if you learn rapier in right, dagger in left TWC, and then for some reason fight with rapier in left, dagger in right, you do get to use your TWC skill, but at -20.
It is not specified that you must have your skill with a weapon in the same hand as the one in which you train it for TWC, so if you allow short sword/ short sword without training short sword (non-dominant hand), that is RAW, but so is requiring training the weapon in the appropriate hand. This is a small gap in the rules.
MAC may have introduced other rules, but except for the question of "Do I need to train dagger specifically for the left hand in order to have a dagger in my left hand for TWC, or is my right-handed dagger skill enough?", the RMSR version of TWC is rather clear. For RM2, I don't think it was consistent, and discussion would have to select a particular version of the skill.
As for multiple attacks with martial arts, that was included in RMSS only in the section for how to use Arms Law without Rolemaster, but if one wishes to allow it (leaving out these capabilities would be a good idea for any GM who believes martial artists are too powerful), the rules in section 5.9.3 of Arms Law cover it already.