What should I use to catch Armored Warriors?

Armored Warrior is a Water/Bug type, so Electric or Flying type moves are effective. Try taking it down with Salamence's Flying moves. Your thorough preparation for victory is admirable.

Usually, when this one Mega Evolves, it becomes Bug/Steel and its ability becomes Tough Claws, so having a Fire-type move should be enough... Since it's slow, you might even be able to catch it with Volcarona?

When Mandibuzz Mega Evolves, its ability makes Normal-type moves also Flying-type.

For Armored Warrior, using a Fire-type that can deal 4x damage with Choice Band is good. I personally use Mega Charizard, which can withstand and defeat Iron Head and Sucker Punch right after meeting.

You can easily catch it using Mega Salamence with Flamethrower or Fire Blast, or Garchomp with fire-type moves.

Armored Armarouge is common even in Mega form, but since its Special Defense is weak, it's good to include something like a Skeledirge or Ceruledge!

No, z-rank weapon shop is also fine.

If Hanka is special type, Fire Blast. For Memelda, whether physical or special type, Fire Blast or Reckless Tackle seems good.

Mega Aggron's only 4x weakness is Fire. There are various ways to exploit this, but an easy one is: Using a Mega Salamence with both physical and special attack stats (ad/ap) and equipping Fire Blast. Since it's a 4x weakness, even if Fire isn't your primary type, using it as a sub-weapon makes the fight easier.

I put Mega on Luca and kill them with Rust Cannon.

Use Githyanki Kithainar

Recommend a Bomanda art supply store

Mega Garchomp Z Flamethrower