Which websites are you referring to? I never noticed any problems from the sites I use. Only when I encounter any kind of captcha I always have to manually select images and it will never solve itself like some did in the past. But not sure if thats due to me not being logged in with Google in my main browser or if it’s caused by Honeygain.
Yes I’m sending all my messages through SMTP2GO or Mailgun and never had any problems with emails going to the spam. Of course using a relay can be an issue when it comes to privacy, but I noticed that in my case I mainly receive emails with private information and only rarely send anything that could be used for tracking.