Is there a way to force my application to run at the background
It's up to the developer of an app to specify what it should do in the background. Apps have two kinds of component. (Actually, there are more kinds, but they're irrelevant to the question.)

The first, activities, can display on the screen, and can only run in the foreground. However, when you leave an activity with the home key, it gets an opportunity to save its state, so when you next run the same activity, it can appear in the same state you left it. (For example, an email app might display the same email you were looking at before, instead of going back to the inbox.)

The second kind, services, run in the background, and don't display on the screen. They have to be written in a different way to activities, to make sure they don't run down the battery, and they have some control over when they start and stop running.

If an app doesn't save its state, or gives an error when you come back to it after using a different app, you should report that to the developer of the app, so they can fix the bug.