You are welcome 🙂
1. & 2. – Both are intended yet. Issue 1. is because of the old design of the statistics. Once we get to the rework, this is going to change a bit, as it will also not the filter states.
The results page search is not recorded on purpose, as it already adds a pageview – where in most cases people use analyitcs or other page tracking, which already does this. I think this will be an option for the reworked version as well.