Hi glad4mercy;
I’d like to throw in my four or five cents here. It took me a while to come up with this and I think I burned up a few brains cells in the process. I hope you would be willing to lend me a few of yours sometime. 
The mouth (i.e. the Antichrist, the beast)
Who is the one who restrains?
I think a clue to this is found in verse 6 where Paul says that “in his time he will be revealed.” [Interesting side note that Paul claims that the one being revealed is a “he.”] In Acts the disciples asked Jesus a question about when He was going to restore the kingdom. Jesus said, Act 1:7 … "It is not for you to know times or epochs which the Father has fixed by His own authority;”
There are obviously set times for certain things to take place according to the Father’s authority and plan.
The father determines not only the boundary of the nations but also the duration of their existence as well.Act 17:26 “and He made from one man every nation of mankind to live on all the face of the earth, having determined their appointed times and the boundaries of their habitation,”
Even the arrival of Jesus was set according to the timetable the Father had set.Gal 4:4-5 “But when the fullness of the time came, God sent forth His Son, born of a woman, born under the Law, so that He might redeem those who were under the Law, that we might receive the adoption as sons.”
There are a couple of interesting verses in Revelation that also seems to go along with this.Rev 1:1 “The Revelation of Jesus Christ, which God gave Him to show to His bond-servants, the things which must soon take place; and He sent and communicated it by His angel to His bond-servant John,”
Rev 4:1 “After these things I looked, and behold, a door standing open in heaven, and the first voice which I had heard, like the sound of a trumpet speaking with me, said, "Come up here, and I will show you what must take place after these things.”
In both verses the important word is “must”. It is the word dei (G1163) meaning “necessary" or “required”. There are things that the Father requires to take place and at certain specific times. One of those things being the man of sin revealed in his proper time (2:6). I think that what restrains him is simply God’s timing, God’s plan. When those thing he has ordained to take place prior to the man of sin being revealed are completed (i.e. in a sense removed from the list of items which must take place) he will then be allowed to come into the open.
I know that in verse 7 what is removed is referred to as “he” yet the words translated for he in this verse are not the same as is used in verse 6 when referring to the man of sin. The word is verse seven can also be “the”, “it” or many other words used to reference inanimate objects. Why it is translated “he” I don’t know. Perhaps someone with greater knowledge of the Greek language could shed some light on this.
How will He be taken out of the way?
(See above)
In what way does the removal of the one who restrains usher in the revealing of the Lawless one?
(See above) When all those things the Father has determined by His own authority which need, must, are required or are necessary to take place are accomplished then the man of sin will be given the green light to proceed (“in his time he will be reveal” vs 6). He will proceed by an all out effort to deceive the world (vs 9 & 10) and if possible even the saints.
What is the mystery of iniquity/lawlessness?
How was it working even in Paul's day?
The Greek word for mystery does not refer to a secrete knowledge or the knowledge of a secrete sin. It is not a knowledge that is unknowable but rather knowledge that is restricted to a certain group of people. This knowledge is knowable only by those who are part of that group. It’s like a secrete society with knowledge that only those in that society has access to. Now whether that knowledge in this case is intellectual or experiential is something else. Here I believe the mystery is experiential knowledge; known (experienced) by those who are participating in lawlessness. The knowledge they are experiencing IMO is deception. You can see this in rest of the passage: false wonders (vs 9), deception of wickedness (vs 10), did not receive the love of the truth (vs 10), deluding influence (vs 11), believe what is false (vs 11) and did not believe the truth (vs 12). All those who practice lawlessness are in fact deceived. Interestingly though is the fact that the deceived do not believe that they are deceived.
It was manifested and working in Paul’s day because those he was writing to were being: quickly shaken (vs2) and disturbed (vs 2) because of someone trying to deceive them (vs 3). The believers were not part of this “secret society knowledge” because they were steadfast in the truth (vs 13) and were not practicing lawlessness. Paul was at that time delivering to them truth in order to keep them from participating in the deception shared by those who practice lawlessness.
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