A few days ago I noticed my phone notify me about my Google play account as if I had changed my password. Yesterday I found out I had been infected with a rootkit and a packet sniffer. I was able to access my Google account. Found no weird logins to my account. So I checked "Devices" and it said "Unable to connect to phone, last time connected April the 6th". So it means someone did something to my account? I mean it's not that easy to log out of my account on my phone is it? I changed my password and my password rest email, so I should be safe?
You should immediately factory reset your phone, then go to Google and go through the Google Security Check-up and verify EVERYTHING (don't skip any checks), and I would also recommend enabling 2-Step Authentication.
After that, setup your phone again and make sure to enable a lockscreen password, and possibly device encryption as well. Do not enable "Unknown Sources" without somekind of quality security package installed.
I would also go through everything on the Sign In & Security page and look for any anomalies.