Is the 'Umrah valid after performing the two rak'ahs of Tawaf at the Maqam Ibrahim without covering the right shoulder, and saying "La ilaha illa Allah" only once in the first Tawaf at Safa instead of three times?

Your 'umrah (definition) is valid, and there is nothing against you. What you mentioned does not affect its validity. Covering the shoulders in prayer is a sunnah (definition) according to the majority of scholars. The two rak'ahs of tawaf (definition) are a confirmed sunnah (sunnah mu'akkadah) and not obligatory according to the majority, and neglecting them does not invalidate the 'umrah. As for omitting some of the prescribed dhikr on Safa, there is nothing in it, as this dhikr is a sunnah and not obligatory, and neglecting it does not invalidate the 'umrah.