Can I show local videos inside the slider?

Yes, you can, but you need the pro version for that. 

You are able to put your video into a video layer or into the background video option of your slide to make it cover the whole slide at any given screen. Also, there is a background video option for the whole slider at the simple slider type's settings, so if you would put the video there, you could have layers on your slides, what you could switch on the slider, while the video would stay and play behind them.

Check out a few examples at our demo slider library