Question

Does the verb, "hamartía" (with any of its conjugations) mean to live apart from Jesus?

Answer 1

Hello

αμαρτία is a noun.  The verb is αμαρτάνω.  In ancient Greek the meanings were:
αμαρτάνω  = αστοχώ  (I miss the target)
αμαρτία = αστοχία  (miss, failure)

The meaning of the word αμαρτία changed with Christianity:  it is the act of braking the law of God by humans.

Here is a very famous ancient Greek quote :
“Το δις εξαμαρτείν ουκ ανδρός σοφού”

Meaning: Making the same mistake twice is not a behavior of a wise man (ie it is not smart to repeat your mistakes).

Answer 2

'hamartia'  (noun) in old Greek meant 'a missed shot, missing the target when shooting.'  The verb is 'hamartano'.  In religious use, the noun means 'error, mistake, sin;' the corresponding verb means 'commit serious error, to sin.'