God does all the work of drawing someone to himself. He seals them by giving them the Holy Spirit, which allows them to believe on him unto their salvation, trusting in him. It is all his work, not theirs. They are essentially a new person. He knows who they will be since he has elected them.
If anyone wants to be saved, there is certainly nothing wrong with calling out to God and telling him that, asking him for salvation and asking to go his way. Who knows, perhaps the desire to be saved is something that God himself put there and God is in process of saving that person. When God is pouring out his Spirit, we read: "And it shall come to pass, that whosoever shall call on the name of the Lord shall be saved."
Not according to Scripture:
Ephesians 1
13 In whom ye also trusted, after that ye heard the word of truth, the gospel of your salvation: in whom also after that ye believed, ye were sealed with that holy Spirit of promise,
14 Which is the earnest of our inheritance until the redemption of the purchased possession, unto the praise of his glory.
Here's the order:
1. one hears the gospel of Christ concerning His death, burial and resurrection for sins
2. one believes, trusts on the gospel of Christ
3. one is sealed by the Holy Spirit guaranteeing them of the redemption, the adoption
No one is regenerated or elected before they are in Christ, God's elect(Isaiah 42).