The following points detailed in this Study Guide seem to answer your questions, and I just wish to highlight some of them, prefacing them with this simple point. Assurance of God’s grace and salvation comes after the event. God graciously saves an individual. Thereafter, the person becomes aware of that transforming grace.
Some of the problems you raise could be due to a person trying to ‘drum up’ assurance where, either, none can exist because the person is not yet justified by God, or they have been justified but are so insecure in themselves and weak in faith that various things can cause them to doubt the promises of God (see Psalm 88:14). In the first case, their vain imaginations deceive them. In the second case, they needlessly torment themselves. In the latter case that would not happen if they kept to “the simplicity that is in Christ” (2 Corinthians 11:3). Paul used that phrase in context of the way Satan can subtly corrupt the Christian mind from “the simplicity that is in Christ.” Herein lies the problem.
‘The Westminster Confession of Faith’ is based upon the Swiss Reformed Churches Heidelberg Catechism of 1562 and I’m working from a book for classes studying the Westminster Confession of Faith, written by G.I Williamson (Presbyterian and Reformed Publishing Co., Philadelphia, Pa. 1964).
Chapter 17 deals with XVIII – Of Assurance of Grace and Salvation (pp 131-136)
1 Although hypocrites, and other unregenerate men, may vainly deceive
themselves with false hopes and carnal presumptions of being in the
favour of God and estate of salvation; which hope of theirs shall
perish; yet such as truly believe in the Lord Jesus, and love him in
sincerity, endeavouring to walk in all good conscience before him, may
in this life be certainly assured that they are in the state of grace,
and may rejoice in the hope of the glory of God; which hope shall
never make them ashamed.
2 This certainty is not a bare conjectural and probable persuasion,
grounded upon a fallible hope; but an infallible assurance of faith,
founded upon the divine truth of the promises of salvation, the inward
evidence of those graces unto which these promises are made, the
testimony of the Spirit of adoption witnessing with our spirits that
we are the children of God: which Spirit is the earnest of our
inheritance, whereby we are sealed to the day of redemption.
After scriptural explanations of those first two WCF statements, four questions are asked of the students: (a) Is man easily deceived in religious matters? Cite Scripture proof. (b) Why did the Pharisee think that he was ‘right with God’? (c) Does the Scripture affirm that there is valid assurance? (d) Is it the duty of believers to endeavour to possess this assurance?
The answers given are: (a) Yes. Jeremiah 17:9, Galatians 6:3. (b) Because he thought that he was better than other men. (c) The Scripture does affirm that there is true assurance. (d) Yes. Hebrews 6:11, II Peter 1:10.
Then follow 9 points for the students to prove – far too much for me to detail here. I will extract a couple of points pertinent to your query. Re. Romans 8:16 [“The Spirit itself beareth witness with our spirit, that we are the children of God”] what proof is there that a false interpretation is given by those who believe in an immediate testimony of the Spirit (apart from the Scripture)? The answer given is that the error lies in expecting an immediate revelation to our spirits that we are saved, when we believe that this witness is by means of the Word. The next point is that the Spirit’s testimony is by enabling us to know first that his Word is sure, and second, that his Word applies to us because we see undeniable evidence of true grace in ourselves. Then come points 3 & 4 in this section of the WCF:
3 This infallible assurance doth not so belong to the essence of
faith, but that a true believer may wait long, and conflict with many
difficulties, before he be partaker of it: yet, being enabled by the
Spirit to know the things which are freely given him of God, he may,
without extraordinary revelation, in the right use of ordinary means,
attain thereunto. And therefore it is the duty of every one to give
all diligence to make his calling and election sure; that thereby his
heart may be enlarged in peace and joy in the Holy Ghost, in love and
thankfulness to God, and in strength and cheerfulness in the duties of
obedience, the proper fruits of this assurance: so far is it from
inclining men to looseness.
4 True believers may have the assurance of their salvation divers
ways shaken, diminished, and intermitted; as, by negligence in
preserving of it; by falling into some special sin, which woundeth the
conscience, and grieveth the Spirit; by some sudden or vehement
temptation; by God’s withdrawing the light of his countenance, and
suffering even such as fear him, to walk in darkness, and to have no
light: yet are they never, utterly destitute of that seed of God, and
life of faith, that love of Christ and the brethren, that sincerity of
heart and conscience of duty, out of which, by the operation of the
Spirit, this assurance may in due time be revived, and by the which,
in the mean time, they are supported from utter despair.
Again, scriptural explanations of WCF points 3 & 4 follow, with 11 questions asked of the students. Some relevant points are that, “The Bible nowhere states that one cannot be saved without assurance. The Bible shows that true believers have sometimes lacked it. In ‘faith’ a Christian has confidence in Jesus Christ as he is freely offered in the gospel. In ‘assurance’ a Christian has confidence in his faith and other graces.”
You asked, “Does the Church have a process to discover” if they are not elected by God. The Reformed church consistently teaches that, until God takes the initiative and justifies an individual, they are unregenerate. It is incredibly simple, really, and in all the Reformed preaching I have heard over 40 years this is what is proclaimed – not ‘a process’ to discover this, but simply what the Bible states. All who attend to Reformed teaching should be in no doubt that they will remain unregenerate until God sovereignly acts in grace towards them, personally. They will know God’s activity in them as they are enabled to respond aright to the gospel message, in faith. They will be given saving faith. Then they will believe unto salvation. This is not ‘a church process’. What they are ‘to do’ is prayerfully heed the preached gospel message about Christ and come to Christ, as he says all weary, burdened souls are to do, for he will never turn away any such who come to him. It’s not the Reformed church that has this ‘system’ of discovery or ‘process’ of gaining assurance of salvation. Heed the gospel; put your faith in Christ alone; believe the promises of God. All the elect do that, by the grace of God. All those not ordained unto salvation will never do that, no matter how many gospel sermons they hear, for their pride will remain resistant to the truth of the gospel. And God alone knows who those ones are.
Your final question about whether the unregenerate can continue in hope even though there is ‘no chance of salvation’ needs clarifying. None of us know whether an individual will never be saved. The repentant thief on a cross next to Jesus was only saved at virtually the last gasp, when it seemed all hope had gone. It had not. His faith in Christ sufficed shortly before Christ died. Reformed Christians exhort all to heed the gospel and leave all judging to God. We cast the seed of the gospel all over the place, even though some will not take root, for it is God who makes it grow. Everyone is unregenerate until God works that miracle of transforming grace in their heart and mind. But when God does that, an individual experiences undeniable evidence of that true grace. Their minds will not be corrupted by Satan’s subtle doubts as they remain in “the simplicity that is in Christ” (2 Corinthians 11:3).