I will try to provide a few thoughts on this for you.
1. Well of course the CANVAS mobile app. 🙂 Seriously, we do a lot of photos of projects in my class, so using the Canvas app definitely streamlines submissions. Beyond that, I know quite a few teachers use Quizziz, which has a very functional mobile app. I've had kids ask if I can implement Quizziz in my class. I have not used it in a while, but Quizlet has an app. You can make sets of flashcards for students, which they can then access and study from on the go.
2. In terms of implementation, I really stress that without me openly stating we are using phones as a class, they should be asking first. We use PBIS and have a point system so I try to award points when students ask, especially when I see others getting out the phone. This is also in compliance with our general district cell phone policy. I generally have not had too many issues with this one. I have also asked that students stay on what we are doing and have been quick to confiscate phones when they get off-task. Walking around helps.
3. I'm less aware of specific communities regarding mobile apps in education. Reddit has a community around EdTech. It is a large community of approximately 23,000 people right now. I would suspect you could do some searches there and find some previous related conversations. I'm sure if you posted there you might get some good input. This might also address your other question as well.
4. Wait, you did not ask a fourth question. But, another thought I had would be related to what you teach. If you are teaching a class that might incorporate computer science, I'd suggest exploring app design. MIT App Inventor is a great starting spot. Lots of tutorials out there that are student friendly. Kids are not just using apps, but learning how to make them. It is beneficial to have both computers/laptops to create the apps on, and separate mobile devices to use for testing. The emulator looses some functionality in comparison. It is both iOS and Android compatible, and works off a variation on Blockly, so very beginner friendly compared to text based coding. I know Flutter is popular for app development, but it is based in text-based coding, which I find tends to turn off some students a bit quicker (I teach at the middle school level).
Hope this helps a bit.