Hi!
Thank you for all the details, it helps us a lot.
1-3. Unfortunately these are not affected by Ajax Search Pro. The results page layout is fully controlled by the theme you are currently using. These are definitely possible via some custom coding of the results page via a child theme. You can try asking the theme developer, it is very likely he will have ready made solutions for most of these queries.
4. With event tracking pageviews are not generated whatsoever. Everything is sent custom events, you don’t have to worry about that.