Être is meant to be precise, where faire indicates roughly the amount.
Ca va faire la quizième fois que je me réveille cette nuit
Means the person woke up once, then once again, then again, they counted and it adds up to about 15 times. It's often an estimation as it's used when the number is large enough for you to lose track, or when you just couldn't keep track.
In your second example, 2 a bit small though, personally I'd start using fait after a few more times. It's not wrong but être would be better here.
The last example illustrates that perfectly : the je ne sais combien means you have lost track of how many times.
Note that the word faire is used as the "=" for sums :
Deux plus deux, ça fait quatre
Deux et deux font quatre
(Two plus two is four, if I'm not mistaken)
The first example is something different completely. The fact that faire can also be substituted with être is a coincidence. It's a relatively isolated, you should be fine by learning just that phrase (If you find a counter-example feel free to edit and I'll edit my answer).