Is it permissible to use used household items—that appear new and clean—and present them as gifts to relatives and friends without informing them that they are used, given the ability to purchase new ones, and is this considered cheating?

There is no harm in donating old clothes and items; rather, they should be given to those who will use them, either as a gift or charity, because that is better than destroying them. It is also commendable for someone who acquires new clothes to donate their old ones. This is not considered donating something bad, but rather something one cherishes.