There's no "one size fits all" answer for this.
If you move the app from memory to storage you'll gain RAM. Maybe that boost in RAM will give the EE more heap space and thereby prevent GC thrashing. That would give you better perceived performance. But maybe it won't and it will just increase demand-paging for your app and hurt performance. Maybe you'll get a little of both and it's a wash.
How would you handle persistence to RAM? That depends on what your device supports for auto-running apps.
Where should you store settings and logs? Again, that depends on the device, the storage, the size, the frequency of access and loads of other things.
Basically the answer for all of these is only going to be found by you testing your actual app on your actual hardware. Try the difference scenarios and collect metrics to see which performs better. That's the only "correct" answer.