Can’t get my contacts to come on my new phone with my iCloud

Is Contacts syncing turned on in Settings/Your Name/iCloud?

Try Settings/Your Name/iCloud and slide off Contacts syncing. Wait a few minutes and then slide syncing on. Allow time for syncing to occur. The sync is very, very slow.

Last resort - have you tried signing out of iCloud, restarting the device, and then sign back in?

See the Apple Support article below. 

Contacts - Troubleshooting iCloud Contacts.    

Selected a contact to send a message but the word ‘mail’ was the only one in the list not bright and of course would not respond to any touch. Can I change that?

Have you tried updating the contact card with the correct information?