On the TWF thing, here's a purely mechanical thought: (I mean, a thought purely about mechanics):
The big problem with two attack rolls isn't that you have a better chance to hit, or do an extra weapon die, it's that you double-up on all kinds of damage bonuses (and with no attack, ac, or save scaling to speak of, advancement in 5e is going mean some big damage bonuses). In fact, in 5e, the better chance to hit of two attacks is no different than with having Advantage.
So, here it goes:
When you attack with two weapons, you roll two dice to attack. If you have advantage or disadvantage, you still roll only two dice.
Normally, you pick one die to represent your primary weapon and one for your secondary.
If you hit with either die, you score a normal hit with that weapon.
If you crit with either die, you score a crit with that weapon.
If you hit with both, you score a special hit that does damage equal to the weapon die of the primary, plus the weapon die of the secondary weapon, plus your usual modifiers (once). IF both hit and either or both crit, the corresponding weapon die is maximized.
If you have advantage while attacking with two weapons:
If you hit with either die, you score a hit with the weapon of your choice.
If you crit with either die, you score a crit with the weapon of your choice.
If you hit with both, you score the same special hit as above. If either or both of the dice are crits, the whole special hit damage is maximized.
If you have disadvantage:
If you miss with either die, you miss.
If you hit with both dice, you hit with the weapon that rolled the highest natural number on it's die - if they tie, you hit with a weapon of your choice. If either of those dice is a crit, you score a special hit, as above. If both are crits, you score maximum damage on the special hit.
I know that seems complicated, but it's really just meshing it with advantage/disadvantage that makes it so. The basic idea is: you roll to hit with each weapon, and roll damage with the weapon die of each weapon that hit, and add modifiers only /once/.
A much simpler alternative is to simply roll to hit once, and add the damage dice of the two weapons together, adding modifiers only once. This would make using two weapons mechanically /very/ similar to using a two-handed weapon.