I think "Kati looks for banks next to the market" should be accepted.
"Next to" is an English synonym for "beside" and is accepted as a translation of "mellett" in other sentences. It ought to be accepted here.
why searching for is not accepted?
Until now, the system accepted "seeks" (often unnatural but not incorrect) for forms of "keres". It's shorter to type. But in this case, it was rejected!