Question: In the statement $\forall x:X \bullet p(x) \Rightarrow q(x)$, does the universal quantifier apply over the predicate q?

i.e. it is equivalent to $$\forall x:X \bullet (p(x) \Rightarrow q(x))$$ or does the implication take precedence, i.e. $$(\forall x:X \bullet p(x)) \Rightarrow q(x)$$

Answer: 
The non-standard notation used is to be deprecated, exactly because it isn't clear how to scope it. 

Suppressing for a moment the restriction on the quantifier, we need to distinguish in standard notation:

> 
> $\forall x(Px \to Qx)$
> 
> 
> 

and

> 
> $(\forall xPx \to Qx)$
> 
> 
> 

The usual convention for dropping outermost brackets would mean that

> 
> $\forall xPx \to Qx$
> 
> 
> 

is allowed slang for the second wff.

Now, there is an alternative old-school system [old-school in standard first-order logic texts, at any rate] for replacing parentheses with dots (as required to fix scope), where we would write instead

> 
> $\forall x.Px \to Qx$
> 
> 
> 

and (again, but now not slang)

> 
> $\forall xPx \to Qx$
> 
> 
> 

But it is bad practice to mix dots and brackets (two different scoping systems), and we shouldn't write your first formula -- dots *and* brackets -- nor the second.

For restricted quantifiers - with $X$ giving the restricted domain - we could in some syntaxes replace $\forall x$ with $(\forall x \in X)$ [or perhaps $(\forall x \colon X)$] thus:

> 
> $(\forall x \in X)(Px \to Qx)$
> 
> 
> 

vs [dropping outer brackets]

> 
> $(\forall x \in X)Px \to Qx$
> 
> 
> 

A lot of work went into perfecting standard notation from Peano and Russell, through to Hilbert, Church and others: there are good reasons not to deviate!
Not an answer, but I was intrigued by the "Church Dot" and as I have "A Formulation of the Simple Theory of Types" *(Alonzo Church, The Journal of Symbolic Logic, Vol. 5, No. 2. (Jun., 1940), pp. 56-68.)* right here, I thought I would do a quick screengrab of his description of the "Dot" in question.

[![Dot Notation explained in "A Formulation of the Simple Theory of Types"](https://i.stack.imgur.com/kiOqe.png)](https://i.stack.imgur.com/kiOqe.png)