The Bible is full of the news that Jesus is coming back to this earth, but it does not teach that He will come back secretly. This doctrine is not Biblical, but is built around the following text:

1 Thessalonians 5: 2 For you yourselves know perfectly that the day of the Lord so comes as a thief in the night.

From this text, it is said that God will come quietly and stealthily and take away His people, but look at the following:

2 Peter 3: 10 But the day of the Lord will come as a thief in the night, in which the heavens will pass away with a great noise, and the elements will melt with fervent heat; both the earth and the works that are in it will be burned up.

Revelation 3: 3 Remember therefore how you have received and heard; hold fast and repent. Therefore if you will not watch, I will come upon you as a thief, and you will not know what hour I will come upon you.

According to the above passages, we can see that this will not be a quiet event, but the idea is of suddenness and unexpectedness, not quietness or secrecy. Let’s look at some of the other texts about Christ’s second coming, and see whether they support a secret event:

Acts 1: 9 Now when He had spoken these things, while they watched, He was taken up, and a cloud received Him out of their sight. 10 And while they looked steadfastly toward heaven as He went up, behold, two men stood by them in white apparel, 11 who also said, “Men of Galilee, why do you stand gazing up into heaven? This same Jesus, who was taken up from you into heaven, will so come in like manner as you saw Him go into heaven.”

Matthew 16: 27 For the Son of Man will come in the glory of His Father with His angels, and then He will reward each according to his works.
1 Thessalonians 4: 15 For this we say to you by the word of the Lord, that we who are alive and remain until the coming of the Lord will by no means precede those who are asleep. 16 For the Lord Himself will descend from heaven with a shout, with the voice of an archangel, and with the trumpet of God. And the dead in Christ will rise first. 17 Then we who are alive and remain shall be caught up together with them in the clouds to meet the Lord in the air. And thus we shall always be with the Lord.

Revelation 1: 7 Behold, He is coming with clouds, and every eye will see Him, even they who pierced Him. And all the tribes of the earth will mourn because of Him. Even so, Amen.

2 Thessalonians 1: 7 and to give you who are troubled rest with us when the Lord Jesus is revealed from heaven with His mighty angels, 8 in flaming fire taking vengeance on those who do not know God, and on those who do not obey the gospel of our Lord Jesus Christ. 9 These shall be punished with everlasting destruction from the presence of the Lord and from the glory of His power, 10 when He comes, in that Day, to be glorified in His saints and to be admired among all those who believe, because our testimony among you was believed.

2 Thessalonians 2:8 And then the lawless one will be revealed, whom the Lord will consume with the breath of His mouth and destroy with the brightness of His coming.

From the above it is clear that the Second Coming of Christ is not a secret, nor is it going to be quiet! It will be a very glorious, visible, noisy and totally non-secret event, and “every eye will see Him”. The great danger about the Secret Rapture doctrine is that it teaches that it doesn’t matter if you’re not ready, you’ll be given a second chance! This is simply not Biblical and can lull many into a false sense of security.

According to all the signs given in the Bible, Christ’s second coming is very near, and we will get only one chance. The rapture is no secret, and don’t be fooled into believing it. One final text:

1 Thessalonians 5: 4 But you, brethren, are not in darkness, so that this Day should overtake you as a thief. 5 You are all sons of light and sons of the day. We are not of the night nor of darkness. 6Therefore let us not sleep, as others do, but let us watch and be sober.

Your second question is answered in 1 Thessalonians 4 above. Let’s look at it again:

1 Thessalonians 4: 16 For the Lord Himself will descend from heaven with a shout, with the voice of an archangel, and with the trumpet of God. And the dead in Christ will rise first. 17 Then we who are alive and remain shall be caught up together with them in the clouds to meet the Lord in the air. And thus we shall always be with the Lord.

It says that all those who have been Christ’s followers will go with Him to heaven, and “shall always be with the Lord”. There is therefore no time of tribulation after Jesus comes. This awful time happens just before He comes and is ended by Him coming.

Daniel 12: 1 “At that time Michael shall stand up, the great prince who stands watch over the sons of your people; and there shall be a time of trouble, such as never was since there was a nation, even to that time. And at that time your people shall be delivered, Every one who is found written in the book.
2 And many of those who sleep in the dust of the earth shall awake, some to everlasting life, some to shame and everlasting contempt.