Questions about the Quick Toss Battle Master Maneuver from Tasha's

I just hit Level 7.

With Quick Toss, I can expend a Superiority Dice and use a Bonus Action to throw a Handaxe with the VEX weapon mastery (that's what I use for ranged attacks). I can add the 1d8 superiority dice to the damage, but I also have Booming Blade. Can I add the additional 1d8 Thunder damage from Booming Blade on the hit in addition to the Superiority Dice damage, and since I used a Bonus Action for this, would I still get two attacks with extra attack, or would it only be one attack, since I used a Cantrip? I also assume that the 2d8 Thunder Damage from Booming Blade would still apply if the enemy voluntarily moves.

TIA

Booming blade says:

You brandish the weapon used in the spell’s casting and make a melee attack with it against one creature within 5 feet of you.

Therefore it does not appear to be used with a thrown(ing) weapon.

Quote from LeoDillon >>

With Quick Toss, I can expend a Superiority Dice and use a Bonus Action to throw a Handaxe with the VEX weapon mastery (that's what I use for ranged attacks). I can add the 1d8 superiority dice to the damage, but I also have Booming Blade. Can I add the additional 1d8 Thunder damage from Booming Blade on the hit in addition to the Superiority Dice damage, and since I used a Bonus Action for this, would I still get two attacks with extra attack, or would it only be one attack, since I used a Cantrip? I also assume that the 2d8 Thunder Damage from Booming Blade would still apply if the enemy voluntarily moves.

Booming Blade is a spell and Quick Toss is a BM maneuver. That's two different concepts that doesn't match or work together in any way.

The good news though is that since the spell takes an Action and the maneuver takes a Bonus Action you could do both on your turn. But it is still two separate things with no cross-over of the effects.

Quote from LeoDillon >>

With Quick Toss, I can expend a Superiority Dice and use a Bonus Action to throw a Handaxe with the VEX weapon mastery (that's what I use for ranged attacks). I can add the 1d8 superiority dice to the damage, but I also have Booming Blade. Can I add the additional 1d8 Thunder damage from Booming Blade on the hit in addition to the Superiority Dice damage, and since I used a Bonus Action for this, would I still get two attacks with extra attack, or would it only be one attack, since I used a Cantrip? I also assume that the 2d8 Thunder Damage from Booming Blade would still apply if the enemy voluntarily moves.

 You can't. 

In addition to BB not allowing a ranged attack, it also doesn't work because the ability tells you to make an attack when you use it, and Booming blade is a spell. It's a spell that causes you to make an attack as part of its effect, but you still have to be in a situation where you can cast a spell to use it.

Thanks, I haven't used Booming Blade for a couple of levels and for close to a year, and totally forgot that I could only apply it to my weapons in non-ranged attacks. I saw Booming Blade on my D&D Beyond character sheet on the weapons and under Actions, but forgot how it worked.