Simply put - can the Monk class use the Dual Wielder Feat with:
Admittedly this is a similar question to this post about Monks and TWF but I wanted to know if there is any difference in D&D 5e? Does RAW cover Monks and TWF in any meaningful way?
Dual wielding requires you to "hold" or "wield" a weapon. You can't wield or hold "unarmed strikes" so they shouldn't count for dual wielding. Otherwise this part of "martial arts" wouldn't be necessary since it basically states that you now (unlike before) can dual wield with unarmed strikes:
When you use the Attack action with an unarmed strike or a monk weapon on your turn, you can make one unarmed strike as a bonus action.
The fighting style "dueling" also speaks for this. I don't think that anyone would argue that this bonus should not apply if you had nothing in your other hand!
When you are wielding a melee weapon in one hand and no other weapons, you gain a +2 bonus to damage rolls with that weapon.
However, since nothing in the monk page states that monks aren't allowed to dual wield weapons there is nothing stopping you from just dual wielding quarterstaffs and getting the bonus anyway.
Yes.
An unarmed strike is a one handed, simple, melee weapon, as such it counts as a weapon for TWF. So for both of your cases, it would be valid.
It's even valid for a non-monk as that strike is available to anyone who is proficient in Simple Weapons. The key is that it's not available to someone wielding a shield, an item or a non-weapon implement in their off hand.
This is not explicitly addressed in the rules, but the way in which it is presented in the weapons table and elsewhere heavily implies this interpretation.
The description of Dual Wielder says that you
Gain a +1 bonus to AC
Use Two-Weapon fighting, even when the one handed melee weapons you are using aren't light.
and
You can draw or stow two one-handed weapons when you would normally be able to draw or stow only one. pg 165 PHB
The description for Two-Weapon Fighting says
When you attack with a light melee weapon you're holding in one hand, you can use a bonus action to attack with a different light weapon that you're holding in the other hand. You don't add your ability modifier to the damage of the bonus attack unless the modifier is negative. pg 195 PHB
The description of Bonus Actions says:
You can take only one bonus action on your turn, so you must choose which bonus action to use when you have more than one available pg. 189 PHB
And the Martial Arts Description states:
When you use the Attack action with an unarmed strike or a monk weapon on your turn, you can make one unarmed strike as a bonus action.
The upshot is that you get the +1 to AC as stated above. Any character can attack with two unarmed attacks provided the second attack is the bonus action. What a monk gets is to add their ability modifier bonus to damage with the second attack. No other player gets that.
But, Dual Wielder is redundant and unneeded. If you put the 2 points it would cost you for the feat into Dexterity or Wisdom you would an extra point of AC, plus whatever bonuses apply to your skills.
