Try resizing the Chrome window to you preferred size, then hold down CTRL while closing the browser (using the mouse to hit "X"). This should save your current window dimensions, 'though it doesn't always work

Yes, when it makes sense. It rarely does though, so for the most part I've only purchased games which I can't get anywhere else (Forza Horizon 3, Forza 7, Gears 4 etc.).

I also much prefer installing certain apps such as Spotify from the store, as opposed to getting it from the developer directly. This way it's completely contained, so that when you're uninstalling it wipes every trace of it from the system. This and easy updates is more or less the only thing I really like about using the store.

I'm thinking this might explain what you're experiencing: https://forums.adobe.com/thread/1654402

[...]Speed Launcher is adding a HKCU RunOnce entry over and over again and assigning a random number to it.  This is then of course alerting WinPatrol who is monitoring new startup programs[...]