I’ll post some verses below but will answer your last question first. We know Jesus Christ did not come to America after the resurrection and before the ascension because there are the four Gospels that talk about Jesus Christ’s time on earth. There is also logistics. There is no way anyone could have traveled from the middle east, from Jerusalem, to America and be back in the short period of time between the resurrection and ascension. Using logic and reasoning it just doesn’t fly. Reading the New Testament should be helpful but I would suggest using a non-LDS bible, and if it makes you feel better don’t use a Catholic one either.
The verses are below. I also provided a link to the USCCB site where I copied the verses. Let me know what you think.
*2 Peter 2:1-3
False Teachers.
1 There were also false prophets among the people, just as there will be false teachers among you, who will introduce destructive heresies and even deny the Master who ransomed them, bringing swift destruction on themselves.
2 Many will follow their licentious ways, and because of them the way of truth will be reviled.
3 In their greed they will exploit you with fabrications, but from of old their condemnation has not been idle and their destruction does not sleep.
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*Matthew 7:15-20
False Prophets.
15 “Beware of false prophets, who come to you in sheep’s clothing, but underneath are ravenous wolves.
16 l By their fruits you will know them. Do people pick grapes from thornbushes, or figs from thistles?
17 Just so, every good tree bears good fruit, and a rotten tree bears bad fruit.
18 A good tree cannot bear bad fruit, nor can a rotten tree bear good fruit.
19 Every tree that does not bear good fruit will be cut down and thrown into the fire.
20 So by their fruits you will know them.
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*Colossians 2:4-8
A General Admonition.
4 I say this so that no one may deceive you by specious arguments.
5 For even if I am absent in the flesh, yet I am with you in spirit, rejoicing as I observe your good order and the firmness of your faith in Christ.
6 So, as you received Christ Jesus the Lord, walk in him,
7 rooted in him and built upon him and established in the faith as you were taught, abounding in thanksgiving.
8 See to it that no one captivate you with an empty, seductive philosophy according to human tradition, according to the elemental powers of the world* and not according to Christ.
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*1 John 4:1-6
Testing the Spirits.
1Beloved, do not trust every spirit but test the spirits to see whether they belong to God, because many false prophets have gone out into the world.
2 This is how you can know the Spirit of God: every spirit that acknowledges Jesus Christ come in the flesh belongs to God,
3 and every spirit that does not acknowledge Jesus does not belong to God. This is the spirit of the antichrist that, as you heard, is to come, but in fact is already in the world.
4 You belong to God, children, and you have conquered them, for the one who is in you is greater than the one who is in the world.
5 They belong to the world; accordingly, their teaching belongs to the world, and the world listens to them.
6 We belong to God, and anyone who knows God listens to us, while anyone who does not belong to God refuses to hear us. This is how we know the spirit of truth and the spirit of deceit.
*Matthew 24: 3-14
The Beginning of Calamities.
3 As he was sitting on the Mount of Olives, the disciples approached him privately and said, “Tell us, when will this happen, and what sign will there be of your coming, and of the end of the age?”
4 Jesus said to them in reply, “See that no one deceives you.
5 For many will come in my name, saying, ‘I am the Messiah,’ and they will deceive many.
6 You will hear of wars and reports of wars; see that you are not alarmed, for these things must happen, but it will not yet be the end.
7 Nation will rise against nation, and kingdom against kingdom; there will be famines and earthquakes from place to place.
8 All these are the beginning of the labor pains.
9 Then they will hand you over to persecution, and they will kill you. You will be hated by all nations because of my name.
10 And then many will be led into sin; they will betray and hate one another.
11 Many false prophets will arise and deceive many;
12 and because of the increase of evildoing, the love of many will grow cold.
13 But the one who perseveres to the end will be saved.
14 And this gospel of the kingdom will be preached throughout the world as a witness to all nations, and then the end will come
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All from this link
usccb.org/search.cfm?site=newusccb&proxystylesheet=newusccb_frontend&q=false+prophets&lang=eng