Sorry, no solution from me, just confirmation of problems. I had Opera browser on two Linux Mint 18.3 laptops, a 32-bit and a 64-bit. I put off upgrading the 64-bit and the latest Opera version is still working fine on it. I upgraded the 32-bit to Mint 19 and Opera completely disappeared. (Some other browsers I had before are still there.) I tried installing Opera twice. Nothing at all happened once and the other time an error (something couldn't install - just leaving the house, don't remember more) was reported. So, still no Opera on Mint 19.