I'm afraid the only general distinction is the one you have already named: do = perform and make = create.
But that is no more than a general tendency; as your examples show, in any specific instance either or both may be relevant, and at some point in the history of the language one has earned more favour than the other.
It's often possible to see a reason why one is used rather than the other in a particular situation, and that's useful for remembering which one is used; but it is of no value in predicting which one is used when you encounter a new situation. For instance:
You complete your homework assignments, which included writing down the answers to a series of questions. It seems that should be 'making' your homework, but in fact the proper phrase is doing your homework. You might remember this by considering that sometimes your homework doesn't call for you to 'make' anything: it might be reading a chapter in your textbook. The important thing is you did the tasks that were assigned.
You agree to act as the fourth person in a game of contract bridge. You would think this would call for 'do', since you are performing a role; but in fact you make a fourth. You can remember this by noting that what you are doing is “making” a complete table of players—would that have occurred to you before you encountered the phrase?
There's just no telling. You have to learn the right term case by case.
Interesting question!
"Best of luck" seems to say, you hope that someone will have the best luck they possibly can with a specific something (or everything in general), such that if there's any part of their experience that's left up to chance, it will go well for them, because they have "the best luck."
"All the best," which I often see as "I wish you all the best," seems to say, you hope that a specific something (or everything) will happen in the best way possible for them, regardless of how it ended up that way.
For example, wishing "all the best" means you don't know whether she'll do well because she studied hard or because the questions were ridiculously easy or because the questions happened to be about the few things she did know from the material she wasn't able to study; you just want her to do well and wish that she will.
On the other hand, wishing "best of luck" is only wishing her good luck, so only applies to situations of random chance. In this case, the questions from Ch. 10 lining up with her potentially low amount of knowledge from the chapter would be luck, and some would say that the test being easy in general would also be luck.
A potential source of confusion: "Make the best of (whatever)" is a very different phrase from "best of luck". To "make the best of x" means that regardless of how bad situation x turned out because of chance, the subject will make every effort to get a good result out of it anyway. This phrase tends to connote that x was something that did have an element of chance and that it went poorly.
So, if I heard someone say, "We'll make the best of our luck," I would assume that they ended up with circumstances that they didn't want, which are either bad or maybe simply strange, but they are determined to utilize what they do have as well as they possibly can.
Hope it helps!
Best Answer
Frequencies
A search of COCA reveals the following frequencies, out of 3,303:
Very clearly, making a mistake is the unmarked form.
I'm afraid that do a mistake/blunder is not attested in the data. In fact, having searched the British National Corpus, the Corpus of Historical American English, and the Corpus of Global Web-Based English, I cannot find a single attestation of I did a mistake/blunder (or any other forms of did, in any tense, person or number).
From this, I'm going to assert that do a mistake/blunder is not well-formed, grammatical, or even used in Standard British or American English. As I don't currently have access to corpora for other variants of English, I can't comment on their usage/currency.
Now, to the differences in meaning.
Definitions
commit
to perform (a crime, error, etc); do; perpetrate
make
to cause to exist, bring about, or produce
So, what are the implications?
commit vs make
Well, firstly, it should be noted that the parentheticals - a crime, error, etc are from the original, and the definition of perpetrate contains parenthetical deception, crime.
Now, while obviously not conclusive, lexicographers tend to put these terms as examples, generally taken from common uses. These are likely to be frequent collocates of commit and perpetrate.
This gives commit a distinctly negative connotation - you don't commit an act of charity, and even though that is perfectly well-formed, using it in that way infuses the act of charity with negative entailments.
Bottom line
Use commit when the act is immoral, illegal, or you wish to imbibe that sense. Use make for more neutrality. Do not use do in situations where native American or British English is expected.