You don't need to store them, in my country you can't even do it has been a great tool to maintain an overview of your money I/O. I tried several apps but only stuck with Toshl, I think its great UX made the difference.
No.
Storing banking credential to 3rd party is something I never do. Biased by DEV/IT work experience.
I build habit of entering transactions manualy via mobile app - also very helpfull stay fully aware of spendings.