Agree with L30Kas7Ro. I am a native English speaker. The eating woman sounds very unnatural. "The woman who is eating stands up" would be the most natural expression. The woman who eats, while it may be technically correct, makes her sound like she has a title- i.e. she doesn't just happen to be eating at that moment but she is known as "the woman who eats." When I have heard expressions in this form- it is usually to describe a characteristic of a person instead of something they happen to be doing in the moment- like "oh, that's the guy who plays guitar" or "yes, that's the girl who runs triathlons." If the guy who plays guitar sits down in the middle of his set- so he can talk to the girl who runs triathlons - I would not think twice.