Is there a way to make a back-up of any application downloaded on Mac App Store? If I want to erase my hard drive and install a system from scratch I don't want to have to download the same application again, is it possible to create a back-up?
Yes, apple includes a program called TimeMachine that backs up your entire hard drive. You can also use Carbon Copy Cloner that clones your drive to another. Both work well and both serve slightly different purposes.
CCC creates a bootable drive and can also back up incrementally
TM is apple's one touch backup app that's incredibly easy to use
If you have no backups going I recommend TimeMachine, not only for your apps but data