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So Jesus said to the Jews who had believed in him, “If you abide in my word, you are truly my disciples..." Jn 8:31ESV
Col1:21-23 And although you were formerly alienated and hostile in mind, engaged in evil deeds,yet He has now reconciled you in His fleshly body through death, in order to present you before Him holy and blameless and beyond reproach—if indeed you continue in the faith firmly established and steadfast, and not moved away from the hope of the gospel that you have heard, which was proclaimed in all creation under heaven, and of which I, Paul, was made a minister. NASB
Rom11:19-24 You will say then, “Branches were broken off so that I might be grafted in.”Quite right, they were broken off for their unbelief, but you stand by your faith. Do not be conceited, but fear; for if God did not spare the natural branches, He will not spare you, either. Behold then the kindness and severity of God; to those who fell, severity, but to you, God’s kindness, if you continue in His kindness; otherwise you also will be cut off. And they also, if they do not continue in their unbelief, will be grafted in, for God is able to graft them in again. For if you were cut off from what is by nature a wild olive tree, and were grafted contrary to nature into a cultivated olive tree, how much more will these who are the natural branches be grafted into their own olive tree? NASB
No. Perseverance in faith is necessary for final salvation, but all those who are truly saved will persevere in faith because they are kept by the power of God through enduring, saving faith (Jude 24, 1 Peter 1:5). We are kept by God's power, not by our own strength.

yes
or else it would make no sense when St.Paul writes that he is working out his salvation with fear and trembling
It's very appparent that that verse isn't to be taken literally, however. It would be impossible, in fact, because if it were taken literally, it would mean that Paul would be saving himself--which even your church doesn't think is possible.
Not to mention the small detail that Paul immediately follows the verse in question with -
13 for it is God who is at work in you, both to will and to work for His good pleasure.
Paul says to "work out" your salvation, not "work for" your salvation. That's a big difference.
But there is nothing in this verse that suggests we could lose our salvation. If that is what he meant then he would have contradicted himself.
ofcourse we believe salvation is from God working within us
but people are also free to reject that salvation
Adam and Eve were created free of all sin and they were able to choose sin and thus break friendship with God
I think the mindset that those who are "truly born again" will not fall away leads Christians into the mindset of judging others and has born much bad fruit in denominations that teach that