I'm just catching up with the thread after not checking for a few days but all of this is easily changed in Settings on the phone.
The drop downs are notifications - you can stop all of that from happening in Settings.
There are no pop ups on the phone, so if you're seeing them, that's on any website you're visiting, which websites do that a lot and has nothing at all to do with your phone. Chrome browser has many extensions to stop popups and block ads.
I've been using smartphones since 2007 when the first iPhone came out and am one of those people who get the latest and learn the latest things, use all OS's, am very tech savvy and have been on the internet since 1992.
It's really not a Pixel issue.

It is the only Android phone that isn't bloated with useless and unnecessary software and the easiest to use other than iPhone.
Unless you get one of those phones like a Jitterbug or just a basic flipphone that only does texts and calls.