Sentence 1. is correct and natural.
By the definition you've linked, "namely" means "you want to give more detail or be more exact about something you have just said".
In this case, "A, B and C" gives more detail about "three subjects".
Sentences 2. and 3. are incorrect, and for the same reason.
For sentence 2., by the definition that you've linked, "i.e." is used "before a piece of information that makes the meaning of something clearer or shows its true meaning". This is not the same as giving more detail or being more exact.
The information that comes after "i.e." should be another way of saying the same thing. From the example in your link:
For all churches decorous dress is required, i.e. no shorts, bare shoulders, etc.
Here, "no shorts, bare shoulders, etc." means the same thing as "decorous dress", but in a clearer way. There is no extra detail added -- it is simply defined.
Your example reworked to correctly use "i.e." could be:
The exam includes the three subjects we studied this year, i.e. A, B and C.
Here, "the three subjects we studied this year" means the same thing as "A, B and C".
"That's to say" has the exact same meaning as "i.e.", so Sentence 3. is wrong for identical reasons, and you can substitute it into any of the above sentences with the same result.