Is it permissible to keep an Ethiopian maid who has a cross tattoo, while she prays and fasts with us?

There is no harm in keeping the maid with you if her presence does not lead to a Sharia-forbidden act. You must advise her to remove the tattoo, especially if it is in the shape of a cross, unless doing so would cause her great hardship and harm. The Sharia guidelines for employing female domestic workers should be observed.