I apologize for the change of notation, but it will simplify things in the long run. Consider sentences (1-6):
║ (1) x=x ║ (4) Hx->M ║
║ (2) ∃x:x=x ║ (5) ∃x:Hx->M ║
║ (3) ∀x:x=x ║ (6) ∀x:Hx->M ║
Notice the difference between the columns: in the first the sentential function is "x = x", in the second it is "if x happens, I will get mad" ("Hx -> M"). Briefly, some informal definitions:
Sentential functions are functions which, when their arguments are supplied, return a declarative sentence. Declarative sentences are expressions that can be given truth-conditions and thus can be evaluated to true or false.
Let g(x) denote "x = x", and h(x) denote "if x happens, I will get mad" ("Hx -> M"), to obtain:
║ (1) g(x) ║ (4) h(x) ║
║ (2) ∃x:g(x) ║ (5) ∃x:h(x) ║
║ (3) ∀x:g(x) ║ (6) ∀x:h(x) ║
This table is just to show how formally similar (1-3) and (4-6) are. Now let's get to the problems.
Claim 1. (1-3) are all equally true.
Expression (1) cannot be true, because it's a sentential function; sentential functions don't have truth-conditions (see the definition above). Sentence (3) says that everything is self-identical, so it's pretty uncontroversially true. Sentence (2) says that there exists something which is self-identical. In order for (2) to be true, at least one thing has to exist, while (3) is true for even empty domains.
In sum: (1) has no truth-conditions, (2) is true in all non-empty domains, and (3) is true in all domains.
Claim 2. (5 & 6) have different truth-conditions.
Exactly! For the same reason (2 & 3) have different truth-conditions.
Question. What's the difference between (4 & 5)?
As I said in my response to your first claim: (1) has no truth-conditions. The same is true for (4); it too has no truth-conditions. (5), like (2), however, does have truth-conditions: (5) is true if and only if: there exists some x such that either: x is not happening or you're getting mad.
Hope that makes things a little clearer.