Ivan,
In answer to your questions:
***EDIT***
When an app is starting up, it looks like this:
No action need from you on the back end, it just starts up.
***END OF EDIT***
Hope that helps,
Mike
1) You can find more details here: https://www.mendix.com/editions/comparison-chart/
You are limited to a set amount of users, there are no limitations in whay you can build. You only have one app container as a total set of resources. Depending on what kind of app you are trying to build and the functionality you are looking for this can be enough.
Back-ups are made on a weekly basis, could be enough or you, but this also depend on how business critical the app is going to be for you.
Sincr it's a free app, the app isn't always on. It needs some time starting up once accesed. It shuts down automatically after 2 hours (could be wrong here on the amount of hours.
2) You can build amazing apps with Mendix, small or large and everything in between. So yes, you should be able to build that custom app you are planning for.