Is it obligatory to repeat the two 'Umrahs from the Miqat for someone who performed them without Wudu, while unaware of the obligation of Dam (atonement) or Kaffarah (expiation)? And is it permissible for him to cut his hair and nails before repeating them?

Purity is a condition for the validity of the Tawaf according to the majority of scholars. So, whoever performs Tawaf without purity is considered as if they have not performed it. The first Umrah remains valid, while the second Umrah becomes void. It is obligatory to cease from the Ihram prohibitions and return to Makkah to perform a valid Tawaf and Sa'i, then shorten the hair. There is no need to re-enter Ihram from the Miqat.

Regarding Ihram prohibitions committed out of ignorance: those that involve destruction, such as cutting hair or clipping nails, require a single Fidyah (a sheep, or fasting for three days, or feeding six poor people). As for those that involve luxury, there is nothing due for them. Sexual intercourse does not invalidate the Umrah according to many scholars if it was done out of ignorance.

If you are unable to return to Makkah, you are considered to be prevented (muhsarah), and you can exit Ihram by shaving or shortening your hair along with sacrificing a sheep or a camel and distributing it to the poor.