No, earnest means characterized by a firm and humorless belief in the validity of your opinions.
The opposite could be insincere, or (for enthusiastic) unenthusiastic or unambitious.
Serious, earnest.
The opposite of 'ancient' is 'modern'.
He was an earnest man. He performed his task in earnest.
earnest
No, "earnest" does not have a prefix in it.
The opposite of the modern era would be the past.
The opposite could be new, recent, modern, or young.
modern
Vintage, old
The opposite could be new, recent, modern, or young.
These words are the opposite of modern: traditional outdated old fashioned antique classic