Protein expression means to clone compounds. Purification is the cleaning process of those compounds. http://en.wikipedia.org/wiki/Protein

Total Activity almost always decreases during protein purification.

Yes, you are correct. Protein expression and purification is definitely a good example of scientific process.

A measure of how much more pure your protein is after a purification step in comparison to the crude. You can calculate this by dividing the purified steps specific activity by the crude steps specific activity.

You have many proteins in a mixture. To identify a single protein you add a GST tag. So, when you are doing any further purification you will end up with your protein of choice.