Is it permissible to use the word "sudfah" (coincidence) in a phrase such as "When I went to the market, I met so-and-so by coincidence"? Is it forbidden or considered shirk (associating partners with Allah)? And what is an alternative for it?

There is no harm in using the word "coincidence" (صدفة), because what is meant by it is meeting a person without prior arrangement, and not without Allah's decree. This word has been used in Prophetic hadiths, such as "So I happened upon him, and he had a branding iron with him" and "We happened upon Aisha, the Mother of the Believers." The Permanent Committee and Ibn Uthaymeen have stated the permissibility of its use, clarifying that "coincidence" expresses something happening to a person unexpectedly, but it does not apply to the action of Allah the Exalted.