# My daughter

Ruth cared for Naomi as if she were her own mother, so Naomi called her “daughter”.

# should I not seek a place for you to rest ... for you?

This question can be translated as a statement. Alternate translation: "I must look for a place for you to rest ... for you."

# a place for you to rest

Possible meanings are 1) a home for Ruth or 2) a husband who would provide a home for Ruth. Naomi probably had both senses in mind.