Welcome to the Q&A Forum

The straight answer to this is NO! You cannot look in to analytics data and see who are visiting these pages and where are they coming from but yes you can always look in to their back link profile and see which websites are linking to those pages and guess accordingly. Just a thought!

I like SEMRush. They give a lot of data about both organic and paid search.

Agree with Umar regarding your speed question. I guess the only other thing you could do is check the forums for questions and concerns raised regarding the theme speed. You'd have to read thru them carefully though to make sure any issues raised are theme related and not something else. As to your second question, you might find this article helpful - https://yoast.com/wordpress-seo-plugin-theme-integration-guide/. It's Yoast's explanation of how to pick a theme that can be optimized.

Great answer!