Will it possible to move the folder along with history and labels within the same collection but different projects.
I've gone through several links and got to know folder history can't be preserved whereas individual file history will be moved. Below is a good article that provides the information.
Still, I would like to know about the labels and is there any documents/links which demonstrate the folder move.
There's no way of moving the folder with history and labels in TFS.
As you already know that folder history will be lost, but the individual file history is actually not lost, It is hidden under the little "expand me" arrow at the far left on a file history line.
For the labels, actually it's dependent on the absolut sources path. So, the label will not be moved with the folder moving. However you can re-label the sources again after the moving.
You can reference below related threads: