Can’t login for iMessage and FaceTime.

Perhaps your Apple ID or something else, is incorrect in this instance.

Had considered a reply to this, but now following does not appear right.

• If you can't send or receive messages on your iPhone, iPad, or iPod touch - Apple Support

//support.apple.com/en-us/HT204065

[While some of ^ it certainly does.]

..How was the replacement device set-up for use with your account?

Some things need to be done first; and curious how this was done..

• What to do before you sell, give away, or trade in your iPhone, iPad, or iPod touch - Apple Support

(For instance, if used product had been readied for new owner? Or, if Activation Lock applies?)