Original description by @Etonkovidova

(1) It seems that the search for a user can be performed only from the first page (the page number 1).

• go to Special:MentorDashboard
• from a default view, search for a mentee that is on the list but not displayed on the first page. I searched for ET14 (listed on the page 5 of the default view) - the user is found.

• go to the second page and perform the same search - the user won't be found

In, fact the user ET14 (listed on the page 5) won't be found from any other page except the page 1 (including the page 5 where the user name is displayed).

Problem

When reproducing this issue, I realized that it also affects filtering, not only searching. That is because the pagination code still remembers it is supposed to show results from 2nd/3rd/10th page, while after applying the filter/search, there are often not enough such pages.

In another words, filtering works perfectly, but it shows results from a page that does not in the filtered set.

Solution

The solution is to reset state of pagination before a search/filtering is performed. That is necessary, because the filtered data will contain different number of users, and thus will need a different number of pages.

Will upload a patch shortly.