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.
All are grammatically correct, but can have slightly different meanings.
You also are allowed to see your son.
This could mean that in addition to other things that you are allowed to do, you are allowed to see your son. Depending on context, it could mean that in addition to others being allowed, you are too. E.g. "Your son's wife is allowed to see him. You also are allowed to see him."
You are also allowed to see your son.
Pretty much the same as the previous. We would be less likely to use this form to say #2 above, i.e. that you are allowed along with others who are allowed. This would more likely mean #1, in addition to other things, you are also allowed, etc.
Also, you are allowed to see your son.
In addition to other things, you are allowed to see your son. This differs from the first two in that it can be used when the other things are not permissions, while the first two would generally be used only to discuss several different permissions. That is, for example:
You are allowed to have a lawyer present during questioning. You are also allowed to see your son.
Versus:
Your deposit will be refunded. Also, you are now allowed to see your son.
Finally,
You are allowed to see your son also.
This one is most different. It would normally be used if there are specifically others that you are allowed to see, and your son is one of those. Like, "You are allowed to see your daughter. You are allowed to see your son also." You wouldn't use this form with other permissions or with other things that are not permissions.
But note that if you put a comma between "son" and "also", then it becomes the same as "Also, you are ..."
Best Answer
For me (1) "make mistakes" is the better phrasing. Also "make a mistake" if there is only one.
Phrase (3) does not read correctly. In that context "mistake" needs to be followed by the type of mistake. Eg "I always mistake verbs for nouns when..."
The only usage of (2) "do mistakes" I can think of is as a question, eg "Do mistakes in grammar lead to ...?"
The first line of the question asks "Do you see the mistake in it?" This also does not read nicely to me. Perhaps a better phrasing would be "Do you see the differences between:" or "Can anyone [please] explain the differences in the following:"