This is a tough question to answer without really getting deep into your app, but I'll take a crack.
Be consistent with primary wayfinding
I think Google has done a nice job with the hamburger-becomes-back approach. It still makes me nervous.
The "menu" button on mobile (whatever form it takes) is about exposing a higher level of navigation. This is most often the overarching structure of your app, superseding where the user happens to be at the moment. Hiding access to this hierarchy feels like a risky move.
Forcing the user to step back out of whatever they are doing to get to the menu is something I avoid wherever possible.
Keep current state navigation in view
Within a view or sub-area of the app, there is context, things that exist solely in that view. Be sure that the user is aware of their place in this context and has a quick path back to wherever their flow may necessitate.
For your use cases 2 and 3, some form of breadcrumb or progress indicator seems like a very sensible navigation metaphor. If that eats up too much real estate, it can slide off screen when scrolling down and slide back in on scroll up.
Save progress whenever possible
When you have a task flow that is likely to be stepped out of at some point, save the user's progress automatically and visibly. This will give the user confidence when the time comes to step away.
For your use case 1, persistent access to the main menu nav will allow them to jump to search or another sub-area as needed. Then switching back to App 1 should recall their position in that view and the state of the form they were working on.
Rainbows and unicorns
Of course, this is all perfect world stuff. You can't always save everything. And you can't predict every possible user flow. When compromises are necessary, just be certain the points of access in your app are consistent. Providing the user with as much recognition over recall as possible will also ease their path to recovery.
