Hello kiwichick, thank you for the feedback.
On 1), that was working in the past -> I see this is not working anymore,
I will investigate.
On 2), the cursor position (= selected bookmark) is retained and shown again when opening. FF and CSS center the view on it, so that might be a little different scrolling position than when quitting, but this should be close enough. Am I misunderstanding what you are saying ?

Note: for reporting issues / bugs, the best is to open them there -> https://github.com/aaFn/Bookmark-search-plus-2/issues
since then it is easy to follow up and to discuss, and to make sure that I can properly address them (this is hard to do on this add-on comment page).

============ update 17/01/2023 ===========
On 1), problem investigated, this was indeed a regression, fixed in 2.0.112 now published.
Thank you.
On 2), ok, thank you, yes this is the best behavior that can be easily achieved with GUI/presentation functions available to the add-on.