Have you checked your Social folder for the missing emails? Gmail started dividing up emails between two folders, primary and social, a while ago, and I must have missed their announcement about it. As a result, I missed a lot of emails which were being saved to my Social folder, which I didn't even know existed.
I hate the way Gmail automatically updates my calendar too. I intend to move away from it as soon as I get my life organised!
RE: Can anyone recommend a good alternative for Gmail? It's time to move...