To pass username and password into GET, make sure you're in SoapUI NG tab because there are Dashboard, Projects, SoapUI NG, Secure, LoadUI NG, and Service V. But in SoapUI NG tab allows you to create parameter. There should be plus sign to add parameter. For the parameter input fields, there will be the Name and Value of the parameter so just enter username and password.
Since the product that I have tested, the Login API returns back when login successful so I can check the return call of JSON. However the developers in my team feel afraid of security risk for returning back the value when login failed so they decided not to return anything.
I was testing a website which I would have to log in to acess some features. I have the open source product, I already did that with the get and add parameters. But when I run it, it just stays in the login page, doesn't login at all to the next page.
You probably have to look at different test option which I'm not sure how to do that in SmartBear SoapUI. I use this tool to test web API only so all of my test cases don't really launch any web application. It seems to me you're testing GUI as well. Maybe someone here knows how to test GUI with SoapUI otherwise SpecFlow with Selenium.