Is there a way to extend cloth cache? If I baked part of the simulation already and want to bake a couple more seconds, i.e. I have 120 frames baked and looks nice so I want to bake the 121 - 240 frames. Is there's a way for me to just do that? Or do I need to start from frame 1 again?

Thanks!
You have to rebake the full simulation. There is some tricks if you are really in a bad situation and really can't rebake fully, such as freezing the mesh as last frame and starting baking from there. But keep in mind there is no way for your simulation to know what was going on prior to the frame your start the baking, so your sim will start with 0 force applied.