Re: "I'm not able to send/receive messages from one contact in the Messages app"
In the Messages app:
iMessages: from Apple to Apple go by wi-fi (blue bubbles).
Texts: To and from Android users require cellular data (green bubbles) (provider-charges may apply)
if needed: View or change cellular data settings on iPhone - Apple Support
Else:
You may want to check you have a Contact card for the contact you don't receive Messages from.
(It is possible you have blocked (spam) messages from all those who are not listed in Contacts.)
If needed: see how to: Add and use contact information on iPhone - Apple Support