1) Currently if I search for something, and I check one occurence and go back I end up at the search screen. (with my latest input)

I would like to go to the result list instead.

2) Could you save the previous selected Search scope and search options? If I select something and go to menu or exit the program, then the default values are used. Perhaps also save the latest search term, as you may easily clear it.

3) A dropdown list for the latest search terms would be great.