Does submission under an unbiblical church affect your prayer life?
1) An unbiblical church will teach unbiblical doctrines / views of God. This will affect your worship (which includes your prayer life), since you are not worshipping God
as the God of scripture. You will worship a god that was fashioned according to the teaching of the unbiblical church and you know the commandment states: "You shall have no other gods before me" (Exo 20:3) - So yes, it will affect your prayer life.
2) Just remember that if it affects your worship, your prayer life is not the only thing that you should worry about. Your whole being as a christian is affected, because your whole life should be an act of worship. " The Apostle Paul says in 1 Cor 10:31 "So, whether you eat or drink, or whatever you do, do all to the glory of God." Every aspect of your life should be an act of worship, ie to the glory of God.
unrepentant sin in my life
1) The fact that you are worried about unrepentant sin seems to indicate that your own knowledge of God and scripture is sufficient to cause conviction. If this is the case, Scripture is clear and have given a clear answer from God already: God
commands people to repent. (Acts 17:30). It is a commandment, it does not hinge on church membership.
2) To repent is to confess your sin and turn from it to Christ. Proverbs 28:13 says: "Whoever conceals his transgressions will not prosper, but he who confesses and forsakes them will obtain mercy." The commandment from God is clear, your conscience is convicting you, so the road is clear - repent.
And yes - I think sin is clouding your judgment by obscuring the real issue (repentance) with church-moving (not that this is not important).