In both cases Imperfective should be used:
- Кто БУДЕТ УБИРАТЬ на этом этаже?
(you were right to pick up the Imperfective here, as the focus is not on the beginning or the completion/result of the action,
but on the doer of the action.)
-- Фекла. Когда она закончит (Perfective, to indicate the completion) УБИРАТЬ (Imperfective)...., она придет к нам.
( here the imperfective just names the PROCESS of cleaning, and the COMPLETION of this process is communicated by the verb " ЗАКОНЧИТ).