A "deal" is a significant but unspecified amount. You can't have a small deal of something, and deals don't have exact quantities. Deal is also much more informal than amount:
- The gravel delivery came and now I've got this great big deal of gravel sitting in my driveway.
- I've got a bill here for half a cubic meter of gravel: is that the right amount?
- The smallest amount this instrument can measure is 300 parts per billion.
(Edited to add a note about your first sentence: "I've just been given a great amount of news - I've passed my exams."
That's really odd. Passing one's exams is only one piece of news, and while "one" is certainly an amount, it's not a "great" amount. It would be correct to say:
- I've just been given a great piece/bit/item of news - I've passed my exams.
In certain unusual situations, you might be able to say:
- These are all the newspapers and news reports I missed while I was on my wilderness vacation: I've just been given a great amount of news.
But that would be much more natural as "a great deal of news.")