The Stack Exchange search does have some advanced tipsadvanced tips (click the "Advanced Search Tips" link to see all of the options).
If I wanted to see just questions, I'd start by filtering out answers from the results, as well as closed questions:
closed:no is:question
Then I could filter further by finding questions with at least one answer, with an accepted answer, and a score of at least twoat least one answer, with an accepted answer, and a score of at least two.
answers:1 hasaccepted:yes closed:no score:2 is:question
To see the last seven days, click "newest" at the top of the search results so they're ordered from newest to oldest. Hope this helps.