Can a Christian gain eternal life?
No:
1) Because they believe they get it from Yeshua's murder; like in the parable of the wicked husbandmen, where it blatantly says God will condemn those who killed his son, thinking they get inheritance.
2) They're like ravenous animals, who hover over a dead body thinking they get reward.
3) A none Christian can follow the words of Yeshua, keeping the commandments, doing good works to gain eternal life.
4) Therefore Christians won't be in the Messianic age.

Can a Christian get their sins forgiven by Yeshua?
1) If they say it was due to him being a human sacrifice, then no, as that isn't kosher and doesn't count for atonement.
2) If they do it from following his teachings and having a relationship with the divine, then Yeshua can help lower the charges by acting as an intercessor.

A Christian is a follower of Paul and Simon the stone (petros), using John's gospel as a foundation; all 3 of those are false, and have led everyone astray.