All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
If the ink is just a colour that does not prevent water from reaching the skin –and this is what we predominantly think –then the ablution is valid and it is not legislated to repeat the prayer again. However, if the ink is a solid matter that can be removed, then it prevents the water from reaching the skin; in which case, the ablution is not valid and you are obliged to repeat the prayer again in the two cases you mentioned in the question. However, what should be taken into account is the prevention of water from reaching the skin; in case it (the ink) does not prevent the water from reaching the skin, the ablution is valid, and if it prevents the water from reaching the skin, then the ablution is not valid and the prayer with such ablution is void.
For more benefit, please refer to Fatwa 83035.
Allaah Knows best.