Question: Could you tell me why angels are doing battle for 21 days before Daniel gets his answer? Also I know the devil imitates the Lord alot, can you tell me if there is a scripture that the devil is imitating God with the mark of the beast on the hand or forehead?
Response: On the Daniel question, this is a remarkable scripture and one of those passages that reminds us that we only have an inkling about everything that is going on in the angelic warfare that must be swirling unseen around us. It also points out that it is mainly the truly exceptional believers that draw this kind of demonic attention. Consider Satan's request to "sift" Peter and the other ten (Lk.22:31), his "incitement" of David (1Chron.21:1) or his "thorn in flesh" aimed at Paul (2Cor.12:7). We're not told exactly why it took so long to help Daniel, although it seems a fair conclusion that the devil made a point of resisting this request from one of the preeminent believers of all time. It is also important to note that despite this demonically arranged delay, Daniel didn't give up but kept at his prayers in spite of such scripturally unprecedented opposition to his request by the forces of the evil one. There is quite a lot at Ichthys on this subject. Please see the following links:
Strangers in the Devil's Realm
The organization of fallen angels (including titles, ranks and functions)
Angelology: the Biblical Study of Angels
David's Disastrous Census of Israel
Angelic Issues I
Angelic Issues II
Satan's World System: Tactical Doctrine
I also think that you are correct in your assumption that the 666 mark is a diabolical imitation of God. This is described in detail in part 4 of the "Coming Tribulation" series, section 3, "The Mark of the Beast". For example, we know that this mark is "of his name or the number of his name" (indicating that all such are the antichrist's property) and this seems to me a direct counter to the re-naming of all who are saved (as special possessions of God: cf. Is.56:5; 62:2; 65:15; Rev.2:17; 3:12; 14:1; - compare the case of our Lord as well: Rev.19:12-16):
They [believers] will see His face, and His name will be on their foreheads.
Revelation 22:4 NIV
Yours in Jesus Christ,