If another player gains control of Hoarding Broodlord, it's still you who can look at and play the exiled card. That player won't be able to look at or play the exiled card.

As long as that card remains exiled, you may look at it. This remains true after Hoarding Broodlord leaves the battlefield.

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.

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.

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

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

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.