However still a bit confused...

I want to use gmail, but of course I also want the website to send and recieve emails using own domain.

I have setup the SMTP with the gmail account and it works.

But, if I send a message with contact form or modify a listing, it does nothing. Probably related to the emails addresses I have put in the Site email field and bug reports email field. The emails I have setup in these fields are redirected to my gmail account in my server.