Is the suitor obligated to return the engagement ring, or compensate the bride's family for the kitchen and carpets after the engagement is broken, knowing that these items are still with them, and that the suitor incurred losses preparing the furnishings?

What you presented to the woman as an engagement ring, if it was a gift and she took possession of it, she owns it, and you are not permitted to take it back. However, if it was part of the mahr (dowry), then you are permitted to take it back.

Regarding compensation for material damage due to breaking off the engagement, some contemporary scholars are of the opinion that whoever causes damage by breaking off the engagement must compensate for it. If a dispute arises, the Sharia court is the decisive authority.