It seems the two problems are related since your slider is adding a layer above the other widgets making them unclickable.
Since the other site which is working is also using the theme then it must not be theme specific but something else in the WP installation or plugin settings.
I see that you’re using some sort of caching or minifying plugins on both sites but they look different looking at the source. Try disabling those plugins first on your test site to see if that was causing the issue. It’s not a good idea to use caching plugins on test sites anyway.
Also, check the contents of the two Custom HTML Widgets above the Slider Widget to make sure that they don’t contain any errors.