Are there specific invocations for Umrah, and what is the ruling on pilgrims repeating invocations after someone who recites them to them, and is it necessary to place the foot and raise the hand at the red line?

Reciting supplications in a loud, collective voice behind the so-called (Mutawwif) is disliked because it disturbs those circumambulating. It is better for the pilgrim performing Hajj or Umrah (definition) to supplicate silently for themselves with whatever Allah inspires them to say, whether it be a reported supplication or otherwise.