Bismihi ta'ala
Muslim women must observe correct hijab, which includes wearing socks, and not showing adornments (zeenah) to non-mahrams. The anklet would be covered with socks, and as for the nose piercing, if it is considered as zeenah, then it would be haram for her to wear it.
If the anklet, or piercing, or any zeenah is considered as exposing in the haram way, although it is a sin, but it will not affect the validity of the wudhu.
And Allah knows best