Does the intention for ablution change when washing a part that has touched the sink, or when washing with the intention of cooling an itch in addition to the intention for ablution, or when intending refreshment or pleasure with the water used to wipe the head, leading to the invalidation of the ablution, especially with the presence of waswasa (whispers of the devil/obsessive thoughts)?

You must repel whispers and not yield to them. The hand does not become impure by touching the sink unless the impurity of the place is verified. If you intend to wash your hand during ablution, without rejecting the intention of ablution, or if you combine the intention of ablution with the intention of cooling off or pleasure, the ablution is not invalidated. The intention of cooling off, cleaning, or teaching does not contradict ablution and does not cause any defect in it. Even if one intends to cool off during ablution while maintaining the intention of ablution, it is sufficient. According to the Hanafis, intention is not a condition for the validity of ablution but for it being an act of worship, so changing the intention to cool off does not invalidate the ablution.