should or CAN I apply to colleges FOR my daughter - time is running out and she has given up on life

I agree with @lookingforward that something is amiss with this story. On another thread you said she is not an international student but is coming from Northern Ireland with dual citizenship and:

If she is going to do a gap year, then time is not running out. It seems a gap year would be a good option while you and she work to resolve her crisis. You mention in that other thread that she may be targeting Harvard. Right now, she is in no shape to be targeting any colleges, much less the likes of the most selective U.S. schools. Focus on getting her back to health; college will take care of itself when she’s ready. Good luck to you both.