Hi Rex,
I hope you are well today and thank you for your questions.
How do I set a featured image for my slider and a different size image for the blog post?
You have to develop custom code to achieve this. Instead of this you can use the pages rather than posts in the slider by using the child theme solution posted in the following topic.
https://colorlibsupport.com/t/two-slider-questions-child-theme/
Also, how can I make it where the items added to the slider do not show in the blog posts. I created a new category (i.e. slider) and I assign a new post to this category only, but it is also showing in my blog posts.
You can try achieving this by using the custom plugin solution posted in the following topic.
https://colorlibsupport.com/t/hiding-posts-from-post-page/
Best Regards,
Movin