Weapon Mastery/Feat Interactions question

It might be spelled out pretty clearly, but I'm dumb, so if someone can help me out with this.

If a character has the Polearm Master and Dual Wielder (allowing one light weapon, and one normal weapon to dual wield) feats, with Weapon Mastery with Quarterstaff and Scimitar, how many attacks can they do?

The Scimitar would allow the extra attack (from the light feature) to be in the attack action, not the bonus action.  So does that free up the bonus action to get an extra attack from using the back end of the Quarterstaff (from Polearm Master)?

EDITED TO ADD:  For clarity sake, it might also help if someone spelled out all the attacks.  So if a character had the Extra Attack class feature, plus all that, would that mean he could do two attacks of either weapon, plus a scimitar attack, on his attack action, plus the bonus action Polearm Master attack?

Two. PAM and DW do not synergize. DW would allow you to attack with your quarterstaff (one-handed, of course) with a bonus action after attacking with the scimitar during your attack action. PAM would allow you to attack with the opposite end of your quarterstaff after attacking with the quarterstaff during the attack action.

Without Extra Attack this would be:
Attack action: Scimitar
Bonus action: DW attack with Quarterstaff
OR
Attack action: Quarterstaff
Bonus action: PAM attack with Quarterstaff

If you have Extra Attack, then you get three:
Attack action: Quarterstaff
Attack action: Extra attack Scimitar
Bonus action: DW attack with Quarterstaff
OR
Attack action: Scimitar
Attack action: Extra attack Quarterstaff
Bonus action: PAM attack with Quarterstaff

If you are thinking that the nick property allows you to move the quarterstaff attack from DW to the attack action to then be able to use PAM on the BA, then that doesn't work because Nick uses the Light property attack and DW is a separate attack (and that's assuming you can use Nick as the first weapon to even do that, of which there is some debate). Nick never enters into this particular scenario that you're describing.

However, assuming your DM is not against the requisite weapon juggling required, you can get 3 attacks in with just DW. You just need another Light weapon:

Attack action - attack 1 some Light weapon
Attack action - attack 2 (from Nick) Scimitar and stow other light weapon
Bonus action - draw Quarterstaff and attack with Quarterstaff (from Enhanced Dual Wielding)

This sequence uses the weapon with the Nick property as the extra attack from the Light property, but if you play it the other way it will still work; just reverse the order of Attack action attacks.

With Extra Attack and DW you get 4 attacks with just two light weapons (one of them being a Nick weapon).

Note that PAM isn't necessary for this.

Edited to include attack options above.

To gain the Polearm benefit the attack with the staff must be first ("Immediately after you take the Attack action and attack with a Quarterstaff, a Spear, or a weapon that has the Heavy and Reach properties") and the bonus action attack must then be taken. If you don't have Extra Attack feature then that's your attack action done.

If you attack with Scimitar first you can attack with the Quarterstaff after that using the Dual-Wielder feature and with Nick mastery your bonus action remains free. But since you did not attack with quarterstaff immediately on taking the attack action then you would not benefit from Polearm master.

That's my reading of the rules. However, if I was DM then I'd houserule it that you get the bonus action attack regardless of which weapon you used first. I mean you took a mastery and two feats to get it - go nuts ma dude.

I find the Polearm Master feat poorly worded and restrictive. I'd rewrite it as: "When you take the Attack action and attack using a Quarterstaff, a Spear, or a weapon that has the Heavy and Reach properties you can take a bonus action and make a melee attack with the opposite end of the weapon. The bonus action weapon attack deals Bludgeoning damage, and the weapon’s damage die for this attack is a d4."

Seems clearer, less ambiguous, allows more freedom of when to take the bonus action, and isn't describing the opposite end of the staff as a different weapon. 

Quote from mechanicalpear75267 >>

 

EDITED TO ADD:  For clarity sake, it might also help if someone spelled out all the attacks.  So if a character had the Extra Attack class feature, plus all that, would that mean he could do two attacks of either weapon, plus a scimitar attack, on his attack action, plus the bonus action Polearm Master attack?

 If you have a Dagger you could;

• Equip Quarterstaff and attack with Quarterstaff [Attack Action]
• Draw and throw Dagger [Extra Attack]
• Equip Scimitar and attack with Scimitar [Nick Mastery]
• Attack with Quarterstaff or Scimitar [Bonus Action]

Edited my original post to include how those attacks all work. Moral of the story: don't take both DW and PAM. One or the other is better depending on what you actually want to do.