There is nothing wrong with your Dell, it will work fine with any MacbookPro. I have been using Dell displays for over 12 years with many different Mac models. I have two 21" Ultra Sharp displays working side by side to design a Keynote presentation right now.
The issue your having is with the way Keynote takes control of the video output to both displays, it sends the presentation signal to one and the presenter display to the other, this is set up in;
Keynote preferences > Presenter display.
If you want to show a wesite or another app on either display, use application switcher:
press the the command key on the keyboard, then the tab key; a row of applications will show what applications are running, choose which one you want to show. Use command > tab to return to Keynote.