If you have a whitespace in front/after a search input you will not find the item (testcase-folder and test-case search). This can happen if you paste a value in the search box.
Ad 1) This should be very easy to implement, we will ship this addition in one of the next versions.
Ad 2) This is actually intended, i.e. that spaces also count as valid search chars. That way you can search for spaces between words.
E.g. test (without initial space) would find both “my test” and “latest update” while test (with initial space) would only match “my test”.