Hebrews 8-10

What is the nature of the new covenant mediated through Jesus?

In the new covenant the Lord will put his laws in their minds, write them on their hearts. The people will belong to God. God will no longer remember their sins.
In the new covenant those that are called will receive eternal inheritance and set free from their sins committed under the 1st covenant.

What did Christ appear at the end of the age to remove? How?

Jesus appeared at the end of the ages to do away with sin by the sacrifice of himself.

We are to consider how to provoke one another to do what? What are we not to neglect that has become the habit of some?

We are provoke one another toward love and good deeds. And not neglect meeting together as some are in the habit of doing.