When deleting messages from Apple's mobile phone, I want to keep the useful messages under the name of one contact and delete others, is that ok?

Of course. Open the email of this contact, click on the top of the email title to be deleted, and the words "Copy more …" will appear. Then click "More" and a blue circle will appear on the left and right of the message. If you want to delete other messages, click the blank circle to the left of the message, and it will turn into a blue circle with a box. After clicking all the messages to be deleted, click the "trash can" in the lower left corner of the phone to delete the messages.