What is the ruling on praying while one's nose is running during prayer and there is no tissue to wipe it, so that one places one of their hands on their nose and is unable to place it on their knee during bowing (ruku'), prostration (sujud), sitting between the two prostrations, and during the tashahhud? And is it permissible to walk to wipe one's nose in a supererogatory (nafila) prayer?

Slight movement during prayer does not invalidate it. One should keep a tissue in their pocket to use if their nose runs. The bowing (ruku') is valid by inclining enough for the hands to reach the knees. Placing the hands on the knees is a Sunnah, not an obligation, and similarly for sitting (julus). As for prostrating (sujud) on the seven limbs and ensuring they firmly touch the ground, this is a condition for the validity of prostration according to the Hanbalis. Therefore, the questioner should avoid prostrating on her knees to avoid disagreement and achieve the complete Sunnah.