iMessage answer is simple, it just doesn't. Same goes for any OS. iMessages don't sync across devices. Prob the most annoying featuring not missing. I can't stand deleting from my Watch after deleting from the iPhone.
Emails shouldn't be any issue. If you delete email from your iPhone and refresh the email on your iPad it should remove them so there may be a setting to change.
But, iMessages/Texts cannot be fixed until Apple changes the the OS.