Q: I have heard that the Holy Spirit will not indwell believers after the Rapture. Will His work cease during the tribulation?
A: The Bible never says the Holy Spirit will be removed from the earth at the time of the Rapture. Some assume that the Restrainer of II Thessalonians chapter two is the Holy Spirit, but even if it is, all this passage of Scripture is saying is that the Holy Spirit will not be restraining lawlessness. It does not say that He will be removed from the earth.
The Holy Spirit will still be regenerating people after the Rapture, indwelling them, empowering them, etc. What He will no longer be doing is baptizing them into the Body of Christ since the body at that point will no longer be here on earth. It is more correct to say that the Holy Spirit will not baptize people into the Body, but He will still be indwelling people.
Q: When is the rapture of the Old Testament saints, both spiritually and physically? I have heard it said that it will be just prior to the Millennium. This does not make sense to me. Who were the saints that were seen after the resurrection of our Lord in the city? Are not the Old Testament saints to be the friends of the groom at the marriage feast of the Lamb, which I understand is to take place during the Tribulation period?
A: There was no actual “rapture” of the Old Testament saints simply because the word itself means “to be caught up” and has to do with the actual meeting of Messiah in the air. What you are probably asking about is the time of the resurrection from the dead of the Old Testament saints, because the term “rapture” applies only to the Church saints.
The resurrection of the Old Testament saints will take place following the Second Coming in preparation for the Messianic Kingdom. You are right that the Old Testament saints are to be the friends of the bridegroom at the marriage feast, but the marriage feast will take place on earth as an inauguration of the Messianic Kingdom. It is the wedding ceremony that takes place in Heaven before the Second Coming, but the wedding feast itself will take place on earth and will kick off the Messianic Kingdom. The resurrection of the saints at the time Messiah died was not the resurrection of the Old Testament saints to immortality, but merely restoration back to natural life, and these people died again later. The reason we know this is because they were raised the moment Jesus died, though they did not come out of their tombs until Messiah's own resurrection. Since no one could be raised into immortality until after Messiah's own resurrection, and since these saints were raised from the dead the moment Messiah died, that would show that they were merely restored back to natural life and not raised to immortality.
Q: I have heard that the Rapture could occur on September 10th, which is the Feasts of Trumpets. Do you agree?
A: Concerning the Rapture, the Bible teaches that the Rapture can happen at any moment, and also teaches that no man will ever be able to set a date for it with any degree of accuracy. Anyone who said that the Rapture will come on September 10 is simply assuming that the Rapture has to come on the Feast of Trumpets. But the truth is that the Rapture does not have to come on any Jewish festival and, therefore, it is a violation of Scripture to set any kind of a date, even presenting it as a possibility. The Rapture will never be a datable event: it can happen at any time during any year between now and the start of the Tribulation.