To you first issue, if the app is running, the parmeters actually don't be changed when clicking a notification with parameters to open the app. From my view, the parameters can only be passed at start of app, a little similar with OnStart. If you want to pass the parameters whenever you want, I suggest you submit an idea to PowerApps Ideas Forum. PowerApps product team would take it into consideration when designing the next version in the future.
To your second issue, I also made a test on my iOS phone, it can still receive the notification when I force closint the app. so for further test, could you share some details with your Flows? Are you the only one meet this issue? What about your colleagues?
If this post helps, then please click on “Accept as Solution”to help the other members find it more quickly.
Thank you for the reply. The flow runs when an item is created on SharePoint and sents a push notification with the title. I set it up to go into batches because of the limitation on the number of recipients (though I have found 5 batches of recipients to work now).
I tested on other Android devices and they hold true as well on Android at least. PowerApps is required to be running to process the notifications (the custom app is not required to be opened) and it can be running in foreground or background to receive the notification, but if the app doesn't run (say after a reboot and it hasn't launched yet) it wont process the notification. This one isn't too big of an issue since the app generally will continue to run in the background on most devices, but a few manufacturers force close apps automatically to save battery life. I have seen this as an issue developing with Ionic Framework as well which is why I tested it, so it isn't as big as an issue as the params only being set at launch.