Would I be able to run test in two contexts simultaneously, like one in the web browser for configuration dashboard and another in mobile device android and iOS.?

Ours is a mobile security application. While doing the test automation of the same, we would be setting up the user, group, application and the device configuration in the web browser based console/dashboard application and the actual test is thus configured will run in the mobile device (real or emulator).

Will it be a problem to model the test case in the testproject and run it ? Either in single run or parallel run method ?

We are in the tool selection stage and we are weighing Katalon, Quantum and TestProject for our project.