So if I have a public key, will my receiver's email service automatically generate a public key for his mailbox so that my letter to him could be encrypted?

No, it would be like shipping a letter to someone on a locked box with the key fastened on the side.

The receiver does not have a public key, so if your provider creates one, it's the provider's key, not the receiver's key. If the provider sends the receiver the private key, everyone in the way can have a copy too. It could not send the receiver the key and decrypt your message and store the plaintext version of it.

It probably only uses the encryption function to send email to other people that are using the same provider as their public keys are available. If you send email to someone that isn't client of your provider, they will only send the plaintext version. So if you want to send encrypted email, you will have to get the recipient's public key yourself and encrypt before sending.

So if I have a public key, will my receiver's email service automatically generate a public key for his mailbox so that my letter to him could be encrypted?

No, it would be like shipping a letter to someone in a locked box with the key fastened on the side.

The receiver does not have a public key, so if your provider creates one, it's the provider's key, not the receiver's key. If the provider sends the receiver the private key, everyone in the way can have a copy too. It could not send the receiver the key and decrypt your message and store the plaintext version of it.

It probably only uses the encryption function to send email to other people that are using the same provider as their public keys are available. If you send email to someone that isn't client of your provider, they will only send the plaintext version. So if you want to send encrypted email, you will have to get the recipient's public key yourself and encrypt before sending.