1) Is it wrong to believe fallen mankind is able to seek God and trust in Christ, in light of God revealing Himself and providing the gospel of Christ?
If mankind is able to seek God and trust in Christ, then why did Jesus say this?
John 6:44 No man can come to me, except the Father which hath sent me draw him: and I will raise him up at the last day.
Matthew 11:25 At that time Jesus answered and said, I thank thee, O Father, Lord of heaven and earth, because thou hast hid these things from the wise and prudent, and hast revealed them unto babes.
26 Even so, Father: for so it seemed good in thy sight.
27 All things are delivered unto me of my Father: and no man knoweth the Son, but the Father; neither knoweth any man the Father, save the Son, and he to whomsoever the Son will reveal him.
It looks to me that no man can come to the son unless the Father draws him AND that the father is the One that reveals His Son to some for how they are able to believe in Him and be saved.
So why does the Father reveal His Son to some but not everyone? Jesus explains...
John 3:18 He that believeth on him is not condemned: but he that believeth not is condemned already, because he hath not believed in the name of the only begotten Son of God.
19 And this is the condemnation, that light is come into the world, and men loved darkness rather than light, because their deeds were evil.
20 For every one that doeth evil hateth the light, neither cometh to the light, lest his deeds should be reproved.
21 But he that doeth truth cometh to the light, that his deeds may be made manifest, that they are wrought in God.
So the Father knows who prefer their evil deeds over those that would come to the light to have their evil deeds reproved and that is why He draws some to the Son to reveal His Son to us so we can believe and be saved at the hearing of the gospel.
We see this happen in the Book of Acts.
Acts 16:6 Now when they had gone throughout Phrygia and the region of Galatia, and were forbidden of the Holy Ghost to preach the word in Asia,
7 After they were come to Mysia, they assayed to go into Bithynia: but the Spirit suffered them not.
8 And they passing by Mysia came down to Troas.
9 And a vision appeared to Paul in the night; There stood a man of Macedonia, and prayed him, saying, Come over into Macedonia, and help us.
10 And after he had seen the vision, immediately we endeavoured to go into Macedonia, assuredly gathering that the Lord had called us for to preach the gospel unto them.
You would think His disciples would doubt that was the Holy Spirit forbidding them to preach the gospel in Asia when that commandment was to go out there and preach Him in all nations, but Jesus did say this.
Matthew 7:6 Give not that which is holy unto the dogs, neither cast ye your pearls before swine, lest they trample them under their feet, and turn again and rend you.
7 Ask, and it shall be given you; seek, and ye shall find; knock, and it shall be opened unto you:
8 For every one that asketh receiveth; and he that seeketh findeth; and to him that knocketh it shall be opened.
So the Father knows whom would receive His Son from those that prefer their evil deeds.
And when sinners are slaves to sin for how and why sin drives them away from the holy God, is why the Father has to draw them unto the Son to reveal His Son so they can believe in Him & be saved.
Faith is a fruit of the Spirit.
Galatians 5:22 But the fruit of the Spirit is love, joy, peace, longsuffering, gentleness, goodness, faith, 23 Meekness, temperance: against such there is no law.
Faith comes by hearing the word hence the preaching of the cross as in the Good News of Jesus Christ. Romans 10:17
Romans 10:17
So then faith cometh by hearing, and hearing by the word of God.
And yet the Holy Spirit come by hearing the word.
Acts 10:43 To him give all the prophets witness, that through his name whosoever believeth in him shall receive remission of sins. 44 While Peter yet spake these words,
the Holy Ghost fell on all them which heard the word.
Kind of brings the whole new meaning to John 3:21 that our believing in Jesus Christ is a manifested work of God.
John 3:
21 But he that doeth truth cometh to the light, that his deeds may be made manifest, that they are wrought in God.
So we can give thanks to the Father in Jesus's name for enabling us to believe in His Son to be saved.