If I send a plaintext e-mail using Gmail to somebody, including my PGP public key block, is that secure?

I’ve been trying to figure out “practical encryption” (AKA “PGP”) for many years. As far as I can tell, this is not fundamentally flawed:

  1. I know Joe’s e-mail address: cool_joe@gmail.com.
  2. I have a Gmail e-mail address: me_78@gmail.com.
  3. I have GPG installed on my PC.
  4. I send a new e-mail to Joe consisting of the “PGP PUBLIC KEY BLOCK” extracted from GPG.
  5. Joe received it and can now encrypt a text using that “PGP PUBLIC KEY BLOCK” of mine, reply to my e-mail, and I can then decrypt it and read his message. Inside this message, Joe has included his own such PGP public key block.
  6. I use Joe’s PGP public key block to reply to his message, and from this point on, we only send the actual messages (no key) encrypted with each other’s keys, which we have stored on our PCs.

Is there anything fundamentally wrong/insecure about this? Some concerns:

  1. By simply operating the e-mail service, Google knows my public key (but not Joe’s, since that is embedded inside the encrypted blob). This doesn’t actually matter, though, does it? They can’t do anything with my public key? The only thing it can be used for is to encrypt text one-way which only I can decrypt, because only I have the private key on my computer?
  2. If they decide to manipulate my initial e-mail message, changing the key I sent to Joe, then Joe’s reply will be unreadable by me, since it’s no longer encrypted using my public key, but Google’s intercepted key. That means Joe and I won’t be having any conversation beyond that initial e-mail from me and the first reply by him (which Google can read), but after that, nothing happens since I can’t read/decrypt his reply?