Everyone is under original sin. A fall so far that on their own they cannot know Christ. John 6:65 informs us the Father has to grant one the ability to come to Christ. I hope that clears things up for you.
No not really because Jesus previously said in the very same discussion
“All that the Father gives Me will come to Me, and the one who comes to Me I will certainly not cast out.”
JOHN 6:37 NASB
All those The Father give Jesus will come to Him but only those who presently and continuously comes to Him He will not cast out. The Greek word used that is translated to comes or cometh is érchomai which is ONLY used in the present and imperfect tense as shown below. So not everyone who The Father gives to Jesus will not be cast away, only those who presently and continuously come to Him will not be cast away.
cometh
G2064
Lemma:
ἔρχομαι
Transliteration:
érchomai
Pronounce:
el'-tho
Part of Speech:
Verb
Language:
greek
Description:
1) to come a) of persons
1) to come from one place to another, and used both of persons arriving and of those returning
2) to appear, make one's appearance, come before the public
2) metaph. a) to come into being, arise, come forth, show itself, find place or influence b) be established, become known, to come (fall) into or unto
3) to go, to follow one
Grammar:
middle voice of a primary verb (used only in the present and imperfect tenses, the others being supplied by a kindred (middle voice) , or (active) , which do not otherwise occur); to come or go (in a great variety of applications, literally and figuratively):--accompany, appear, bring, come, enter, fall out, go, grow, X light, X next, pass, resort, be set.
Now with that being said Jesus also said
“And I, if I am lifted up from the earth, will draw all men to Myself."”
JOHN 12:32 NASB