Just wanted to ask if it is permissible to apply the “Halal” nail polish or permeable nail polish and pray? These nail polishes are not water resistant and will let the water pass through. Also these companies are carrying Halal signs with them for authenticity. What is the ruling regarding this issue from our perspective?

If you are convinced that the water is reaching the skin then it is allowed. But it is up to you to investigate and research whether that is the case.