Easy. Let’s start with:
#slider, #twitter-feed{display:none}
.home #slider, .home #twitter-feed{display:block}https://startupwp.com/topic/customizing-your-theme/
If you want to proceed with swapping out the Twitter widget for something else, this will require hacking the code via a child theme:
https://startupwp.com/topic/child-theming/
If you’re comfortable with that, let us know once you’ve set it up and we can instruct further.