What is the punishment for a shaykh who swore a false oath (yamin ghamus) that he is impotent, despite medical reports proving otherwise and his wife's acknowledgment of their intercourse and her pregnancy? And is his wife entitled to claim her marital rights after his claim is proven false?

If the husband chooses to retain his wife, she has all her rights, unless she is disobedient (nashizah), in which case she is not entitled to maintenance until she returns. However, a pregnant woman is entitled to maintenance for her pregnancy, even if she is disobedient. It is advised to take the case to the Sharia courts or attempt reconciliation. As for the sin of swearing a false oath, it is grave, especially if it leads to usurping a Muslim's right, and it is considered among the "al-yamin al-ghamūs" (the plunging oath).