When talking to a non-mahram woman about a necessary matter, can a man look at her, and can he smile/laugh if something is funny because she smiles/laughs or greets him with a smile, since looking away from her with a still face is awkward and disrespectful? how should a man navigate this situation?

Ustadh AbdulAziz al-Haqqan

This is free mixing and it is not allowed in Islam. Lowering your gaze and speaking normally and respectfully is what is required, and that is not rude.