It sounds like you’re inserting a clip. When you insert a clip it moves everything down to the right. If you don’t want everything to shift do an overwrite edit but the new clip is going to cover up some of the clips or clip already in the timeline.
What I meant by you can’t do this in final cut is that in additon to final cut another application would have to be used also like motion or photoshop like you just said you did
This is a very easy effect to do and it doesn’t use a green screen. You can’t do it in Final Cut you need to use Motion or After Effects. Make a 3 to 5 second freeze frame of the part of the video you want to use…drop it in after effects or motion then double the layer and using the biezer tool garbage matte the person on layer 2 after you cut out your person any video you put above layer 2 will cover up the person garbaged matted any clips you put between layer 1 and 2 will be behind the person garbaged matted. Experiment with differnt color effects textures and motion to get the look you want..good luck