If I uninstall my katalon studio and again reinstall it and login with the same user, then can I restore my previously written test cases?
Your test cases are stored in your project folders which are physical folders existing on your machine. You can use Katalon Studio to open these project folders and use Katalon Studio to develop the Test Cases. So uninstalling and re-installing Katalon Studio should have no effects on your Test Cases, provided you have them stored as a project somewhere on the machine.
With a side note: if ‘somewhere’ is katalon installation folder, you are screwed