In the name of Allah ,the Most Beneficent, the Most Merciful

Nail Polish.

Nail polish for Muslim women is not considered haram if it is made up of halal sybstances.. However nail polish's are usually impermeable to water (i.e does not let water seep through onto the actual nail surface). Therefore nail polish has to be removed before doing wudhu or ghusl.

After having done wudhu or ghusl you may put nail polish them back on if you wish. However every time you need to renew your wudhu or make ghusl you must remove the nail polish.   This could be very difficult and time consuming process. So alternatively you could use henna which is permeable to water and thus you may do wudhu without removing it.

Permeable means that it lets water reach your actual nails and skin. Impermeable means it will not allow water to penetrate it and reach the nails and skin.

Nail polish's and Henna are a source of beautification and thus you need to wear gloves  in presence of of non Non Mahrem men or when outside. Ofcourse the ideal Muslimah dress is that you cover your hands in the presence of non -Mahrem men or when outside even when you do not have this sort of beautification.  About hand covering this is explained in the following article

 Ideal Muslimah's Dress