Messages: Online status or Last seen time Is there any method for me to know if a user registered with Messages is currently online? Or, is it possible for me to determine when they were last seen?

If not is there a way to find out using different method, preferably without reaching out to them?
No. Messages (formerly iMessage) doesn't have any of these features.

Since the feature is not available, there is no way to obtain either of the information by any means.

However, delivery time and read receipt with time (if enabled by the recipient) feature is available in Messages and is shown just below the message bubble.