Once an ability of a planeswalker is activated, it doesn't matter if the planeswalker loses that ability. That planeswalker has still been "activated" that turn.

A planeswalker was "activated" during a turn if one of its abilities was activated that turn. This includes its loyalty abilities and any other activated abilities it may have. That ability may still be on the stack, or it could have resolved, failed to resolve, been countered, or have been removed from the stack some other way.

Emblems are separate from the planeswalkers you got them from. Activating an ability of an emblem doesn't cause any planeswalker to be "activated."

You can tap any untapped creature you control to convoke a spell, even one you haven't controlled continuously since the beginning of your most recent turn.

Tapping a multicolored creature using convoke will pay for or one mana of your choice of any of that creature's colors.

Because convoke isn't an alternative cost, it can be used in conjunction with alternative costs.

If a creature you control has a mana ability with in the cost, activating that ability while casting a spell with convoke will result in the creature being tapped before you pay the spell's costs. You won't be able to tap it again for convoke. Similarly, if you sacrifice a creature to activate a mana ability while casting a spell with convoke, that creature won't be on the battlefield when you pay the spell's costs, so you won't be able to tap it for convoke.

Tapping an untapped creature that's attacking or blocking to convoke a spell won't cause that creature to stop attacking or blocking.

When calculating a spell's total cost, include any alternative costs, additional costs, or anything else that increases or reduces the cost to cast the spell. Convoke applies after the total cost is calculated. Convoke doesn't change a spell's mana cost or mana value.