What does this mean - what would happen if I pressed 'Verify Message' button?
It'll probably ask you for
a message to verify.
I'm a little anxious, because earlier when I tried to use the Bitcoin in my Blockchain account a popup appeared and asked me to tap it to transfer the Bitcoin to the wallet from my address, unfortunately I did tap it and I regretted this action immediately, because I lost more than 10 $ by tapping it.
It sounds like a transaction fee. That's normal, but
customizable.
What should I do, which 'Action' could I choose that would maximize the amount of Bitcoin I can use?
I'd export the private key, use Electrum, and manually set the fee.
If I choose the 'Send' option I can send the full amount of Bitcoin (minus the transaction fee) to an another Bitcoin address?
Probably. But you're using a wallet that isn't recommended and is the source of many topics here about problems it causes. So it's better to never use them again and export your keys.