Is it permissible to analogize a slight release of gas (yaseer ar-reeh) to a slight amount of impurity (yaseer an-najasa) that is pardoned? And would performing the prayer in this state be considered invalid or subject to interpretation? What is the evidence for differentiating between a slight amount of impurity remaining in the exit point and a slight amount of it on another limb?

Those who advocate for pardoning a small amount of impurity absolutely base their argument on the difficulty of avoidance, and not on the Prophet's ﷺ urinating while standing. For his ﷺ urination was in a manner that ensured no impurity would touch him. As for the traces of istijmar (cleansing with stones/paper), the correct view is that it is impure but a small amount is pardoned in its original place. However, if it transfers to the clothing or body, it is not pardoned. As for wind (passing gas), it is pure and does not soil wet clothes, but wudu' (ablution) is required upon its emission, whether little or much.