I cannot add any transitions to my time line

It would be good to see that screenshot. There was a problem like this in earlier versions. Select the edit point and double click the transition in the transition browser to apply it. You might also want to reset your preferences by holding ⌥ ⌘ as you launch the application.

What OS and FCP version are you using? Please post a screenshot that shows what you’re doing where. How are you adding the transition with drag and drop, or a keyboard shortcut, or double clicking it?