Can Akshan use Weapon Master when played to equip friendly gear and then also steal gear and equip that all at once?

Yes, Akshan can perform both actions—using Weaponmaster to attach an Equipment you already control and using his "When you play me" ability to steal an enemy's gear—within a single chain resolution sequence.

How this interaction functions

When you play Akshan, both his Weaponmaster keyword and his "When you play me" ability trigger simultaneously. According to Rule 383.3.d, when multiple triggered abilities trigger at the same time, you may place them on the chain in the order of your choice and resolve both.

1. Weaponmaster (Keyword Effect): As a Play Effect, this triggers when the unit is played. You may choose an Equipment you currently control and attach it to Akshan.
2. Akshan's Ability (Triggered Ability): This is a separate "When you play me" triggered ability. If you pay the [C][C] cost, you move an enemy gear to your base (gaining control) and attach it to Akshan upon resolution.

Resolution

Because you control the order of the chain, you can resolve these in whichever sequence you prefer:

• Resolve Weaponmaster first: You attach your own Equipment to Akshan, then resolve the theft ability to steal and attach the enemy gear.
• Resolve theft ability first: You steal and attach the enemy gear, then resolve the Weaponmaster effect to attach your own Equipment.

Both effects will resolve successfully provided all targeting and cost requirements for each individual effect are met.

Note: I could not fully verify this ruling against the retrieved rules.