Is using nail polish that allows water to penetrate permissible (halal), and is ablution (wudu') valid over it?

If nail polish is merely a dye that does not form an insulating layer, then it does not prevent water from reaching the nail, and ablution performed with it is valid. However, if it forms a layer that prevents water from reaching the nail, then it must be removed before ablution.

Since we do not know the composition of this polish, we will limit ourselves to stating the jurisprudential rule: the condition for the validity of ablution is the flow of water over the limb, not merely wiping it with moisture.

The Prophet, peace and blessings be upon him, commanded anyone who left a spot not touched by water to repeat their ablution and prayer.

It is advisable to ask specialists and trustworthy individuals to determine the nature of this polish. And assuming it allows water to pass through, its designation as "Islamic nail polish" does not permit a woman to go out with it in front of non-mahrams because it is an adornment.