I’m not sure if this is how or where to submit the question, but I could not find anywhere on the webpage to ask a new question, and this won’t fit on Twitter. So, monk martial arts says three things:

1) The monk gets to use Dex instead of Str for unarmed strikes and monk weapons. This is clearly a SUBSTITUTION and thus applies in any case where Str would have created a bonus.

2) You CAN (but do not have to) roll the martial arts damage dice instead of the normal 1 dmg for unarmed strikes or the normal damage for the monk weapon. This is an optional substitution, and I note it does not say roll the martial arts damage dice plus the dex/str bonus.

3) When a monk makes an unarmed strike or monk weapon attack, the monk may make an unarmed strike attack as a bonus action.

So, thus far, if my level 3 monk kicks someone, the monk gets to do a d4 instead of 1 damage due to Rule 2 above. Further, my monk can add either Str or Dex bonus to the attack, whichever is better due to Rule 1. Finally, the monk can add the Str or Dex bonus to damage as well, also due to Rule 1. The question arises with the bonus attack supplied by Rule 3.

Two-weapon fighting (p. 195) says that when you attack with a light weapon, you can attack with another light weapon but without the damage bonus from the ability modifier. The only way to get that modifier is if you have the fighter-type dual weapon style.

So, when my level three monk goes to make his follow-up unarmored strike allowed by rule three, does she get to add her Dex to the strike’s damage like she does with the first attack? (There are two ways of seeing this: You can see it as the monk getting the dual weapon style for unarmed strikes without the book saying so explicitly, or you can see it as the loss of the ability modifier from the two-weapon rule only applying to WEAPONS.) Or does the fist used in an unarmed strike count as a melee weapon, and thus the monk does not get the ability damage bonus on the bonus action attack?

Follow-up: If the two-weapon rule is limited only to weapons and not fists, does that mean that Joe Fighter (level 1) who most certainly has two fists, can choose to attack in a given round with each of them just like if he were holding two shortswords, but then, because fists don’t have the two-weapon-bonus-attack-loss-of-ability-bonus-damage rule, does he also get to add his Str to the damage for both punches? In other words, if fists are weapons, does that mean everyone can a) dual wield fists and b) get the appropriate ability damage bonus to both punches?

I know this was long, sorry about that. Thanks.
Strong MoDan
Don’t worry about lenght of your questions, this is the right place.
I hope to give you the right answer, otherwise I encourage people to give you “the sage advice”.
I start your answer with PHB p.7 golden rule: “Specific Beats General”
In this case “Specific” is Martial Arts description in PHB p.78 that beats “General” Two-weapon fighting combat rule PHB p.195.
Unarmed strike is not considered a light weapon as Master Mike write:

Unarmed strike light

is an attack that you can make in a bonus action, so Yes you can add dex or str as first attack.
Is like fighetr extra attack but fighter can make it in the attack action while monk can do it in bonus action.
About Joe fighter, yes he has 2 fists and two feet and an hard head too but all this parts are not considered multiple weapons but just unarmed strike (PHB p.149 table) that Joe can use normally once in a turn.
Take a look to Master Jeremy answer https://www.sageadvice.eu/2014/09/25/unarmed-kick-elbow-head/
Finally my advice is to read some advice about Unarmed combat https://www.sageadvice.eu/?s=unarmed
“Namo Mituo Fo”