A useful post. I just wanted to add the following quotations which I did not see mentioned.
Hebrews 11:1 Now faith is the substance of things hoped for, the evidence of things not seen.
Our belief, does not not mean we should not have faith.
Hebrews 11:6 But without faith it is impossible to please him: for he that cometh to God must believe that he is, and that he is a rewarder of them that diligently seek him.
Chapter 11 of Hebrews is all about faith. Incidentally, the number of occurrences of the word "Faith" to the occurrences of the word "Believe" is around the ratio of 2:1 in the whole of the Bible. The word "Belief" occurrs once. These numbers are based on the KJV.