If you’re new to Qlik Sense, start with this Discussion Board and get up-to-speed quickly.
Not at the moment. For the time being, if you would like to cycle through dimensions on any UI object in Qlik Sense, you can drag-and-drop any field name (or a master dimension item) from the left taskbar in edit mode, and drop it into any table or chart. A pop-up will then appear and ask if you would like to replace the current dimension.
To replicate this functionality you could create a island table with the cycle group values. E.g. Blue, Red, Yellow
Then in your expression code you have a conditional statement to refer to the selected value of this island and act accordingly.
I have added an extension object to make this a little easier. As Damien suggests, it requires a data island of the list of dimensions you want to use. The extension is just a variation on the horizontal list box that makes it a bit nicer to display the list of options.