Do I continue earning rewards while unstaking?

Yes. If you unstake, the quantity you unstake will continue to earn rewards until the unstaking (i.e. unbonding) period is complete. Your position will stop earning rewards once it is returned to you as the liquid, tradable ETH.

Regardless of the staking rewards being consensus rewards or other rewards, the rewards you receive on the unstaked amount will be allocated to your availability balance of that cryptocurrency.

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Why was my dividend accrual reversed?
Can I sell or trade my crypto while it is staked?
How long will it take for my position to be unstaked?
What happens to my staked crypto if the price changes while it's staking or unstaking?