Is expiation (kaffara) obligatory, and is it considered a sin to pray with doubt about menstruation after bloody discharge and the husband's approach during the period of doubt?

The maximum duration of menstruation is fifteen days. If the blood the questioner saw was within this period, then intercourse is not permissible.

A woman is considered to be experiencing istihada (non-menstrual bleeding) if the total number of days of bleeding and purity exceeds fifteen days.

As for the intercourse that occurred, there is no sin or expiation for it due to the ascription to a possible interpretation (ta'wil) and the lack of certainty regarding the presence of menstruation.