Some Problems With (Instantiation in) Logic

In logic there are two kinds of laws of instantiation: the same should be replaced by the same, and the different should be replace by the different. Logic itself demonstrates violation of both of those principles.

Let's take a look at those three of logical formulas:

a) p → (q → r)
b) (y)Fy → Fx
c) A → (y)Fy

Let add some definitions which are presumed to be instantiated into formulas:

d) r = p
e) y = x
f) A = Fx

If to instantiate the definitions into the formulas matching in this correspond way them: d)→a); e)→b); f)→c).

g) p → (q → p)
h) (x)Fx → Fx
i) Fx → (y)Fy

Important to note, these are three types of different situations without the instantiation: 1) ambiguity; 2) correctness; 3) incorrectness. Which of them are here? 

In (a) we have the next one: a plain functional non-tautology becomes a tautology (in (g)) after the instantiation. However, this might be (1) in case of (d). And what does it mean that d)→a) is correct? This mean if in a certain tablet of values the columns or rows of them can be matched perfectly:


As you may see in this case (for this given tablet) the values of p and r are matched perfectly. Let's take a look at the next example of (b). If y = x, then the formula is (2), or it is correct. However, as the matter of fact y is not x. I mean it may be a confusive. Looking at the formulas of (y)Fy → Fx and (x)Fx → Fx one rather say they are different. As we've seen it with the tablet above, here's the same, but this time p can be matched to x, and r to y.


Another example of A → (y)Fy (c) represent a formula that can be changed violating no rules in logic into (i) Fx → (y)Fy. They say, this last formula is correct, but how on Earth I can see this taking into account the previous example of (h)? 
And most of logicians (the founders of the logic) said that if in (c) A doesn't have Fy, then (c) is correct. Again, let's turn to the previous tablet. What barriers me to write Fy → (y)Fy instead of Fx → (y)Fy?

To clarify all the above I wanted to point something that we've got some ambiguity with the instantiation, and this problem can be viewed using the tablet method. Along with it, there is something I'm gonna to add down below.

Take closer to (a) and (c). Why we're allowed to change A to Fx, having no permissions to change r to p? Why so? Because the principles (from the beginning of this text) lures some ontological or metaphysical principles are not viewed by default. Which ones? - It's about a whole and its parts. If we take a tablet to check this, by default we're assuming that the whole is our central point, and there are no logical regions or areas; instead, localizing different values we can aim them separately without being afraid of doing something risky. So, the localization allows us to move further into logic: because this what does help logician to prove their formulas (for instance, lacking (b) or (c) leads to having less formulas, and therefore a really poor method for formalization the reality). If we want to skip that localization choosing the whole as the main point, then there should be not allowed none of those principles. Indeed, the tablets demonstrate that if let's say x and y are the same, both of them occupy some z so, in turn, it leads to cutting some formulas out.

Summing this: we've got some problems with that instantiation, and those problems lead to some ontological or metaphysical problems, and it doesn't seem that some states of affairs in logic are clear and obvious.