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For #1, just reboot your phone and the toast notification will be gone forever.Hi!.. I bought the Pro version and am happy with it. I've experienced 2 weird things:
1- Sometimes just after unlocking phone a message on the bottom of the screen appears saying that I've already purchased the app. It's as if a "purchase Pro" button has been pressed. This happened to me several times.
2- I use the "AOD off" setting with the proper ADB command activated,: Sometimes when the screen is off the AOD is turned ON but there's no notification to show that causes that.
I don't really use the Hey Google very much but since I saw this post I've been using to test. I haven't had an issue with it. There are a ton of settings and perhaps one of them is kicking it out. Are you stock? You can email the dev and I'm sure he'll respond. Even though it's not open source (50+ apps I have are not OS) his ranking in the PS is beyond reproach so I don't think that should be an issue. Under "general" is your wakescreen on incoming notifications enabled? See if you can figure it out and post back with a solution if you can. Good luck.