I have an program made in qt creator, fully functional, how do I port it to plasma 5 widget/plasmoid?

Or do I need to remake it in plasmate?

How do I add it to the system tray?

If you used QML to begin with, you'll have to use the Plasma QML components instead.

If you used QWidget, you'll also have to switch to QML (and probably redesign parts of it, since what works in a standalone application won't work as well in a Plasma widget).