Carol,

In answer to your question below:

1)  Why does Revelation 3:5 say He who overcomes shall be clothed in white garments; and I will not ERASE or BLOT or REMOVE his name from the book of Life?

The New Living Translation study bible, gives a clear explanation at:

Revelations 13:8........And all the people who belong to this world worshipped the beast. They are the ones whose names were not written in the Book of Life before the world was made-the Book that belongs to the Lamb who was slaughtered.

This is mentioned in Revelations chapter 13, where the BEAST is the main topic. An overcomer is one who overcomes this worlds BEAST system of worship called (Babylon the Great), set up by Satan himself, to mislead all mankind into worshipping him. To overcome this system, one must except Jesus Christ as the True path to salvation, and hold to your convictions, even if it means persecution, tribulations, and even death. 

During the end times, as we are facing now, this also means, NOT taking the mark of the beast! 

White is the sign of spiritual purity , belonging to Jesus Christ as his. The altimate prize of overcoming is to be written in the Lambs Book of Life.

Many are the beliefs of what it means to worship the beast. Obviously, one clue is that they are people who belong to this world. Another is that they worship the beast. The beast is two fold, it is a satanic system of worship that started at the tower of Babel and continues to this very day. And, in the end times, which we now live, it is also a mark, or number (666) that represents the antichrist, false prophet, and the devil himself. 

So, obviously, one must be very careful as to WHAT and WHO one is worshipping by their actions. A good study of Biblical History will make it clear. 

May God bless you in your studies,

Mike P