Is it permissible to perform two Umrahs (for oneself and, for example, for one's father) with a single Ihram without Tahallul, or is it obligatory to assume Ihram from the Miqat for each Umrah?

It is permissible for a Muslim to perform Umrah for himself and then for someone else, but with two separate states of ihram. So, he enters into ihram for himself and performs Umrah, then he enters into ihram for his father from the nearest point outside the Haram, such as Tan'im (Masjid Aishah).