"how to close weblow dropdown by click". Try the ideas her (If it not work for you update):
issue 2 & 3 - mixitup-control-active
When a filter or toggle control is clicked and becomes active, MixItUp will add an “active” modifier class to its markup for styling. By default, all controls receive the active class 'mixitup-control-active' , but this can be customized via the classNames configuration sub-object. Docs
Step-1: Create style for mixitup-control-active (Blue background for example).