How to move the staking rewards into my Wallet?

Never seen it. Maybe, because I never emptied wallet, while using Daedalus. Could you show a screenshot of the warning?

Yes, the rewards are in the total balance and if you send out everything that should include the rewards.

The protocol itself does not have a 10 ADA minimum, anywhere, as far as I know.

But:

  • If you move everything somewhere else, you will still continue to get (maybe considerable) rewards for three more epochs. In order to withdraw them, you will need some ADA left in the wallet for the withdrawing transaction, but 2 ADA should really be enough for minimum transaction volume plus fees.
  • Your stake key is still registered. In order to get the 2 ADA deposit back that you paid when delegating for the very first time, you will have to deregister the stake key. This will stop all pending rewards, so it should only be done after waiting those three epochs for them. That operation will also need around 2 ADA in the wallet for input and fees (can be the same as for withdrawal of the last rewards). Some wallet apps – Eternl, Yoroi – can even do it in the same transaction, while others – Typhon – require you to do the withdraw first and only then the deregister.
  • But Daedalus does not even allow the deregistering operation. They had it: Ho do I UNdelegate? - #15 by Alexd1985 But then they removed it and it never came back in one and a half years. So, they perhaps want you to never get back the deposit? Only solution I know (but that should work flawlessly): Import your wallet to another, better wallet app – Eternl, Typhon, … – and do it there.