confusion about pH of a substance
Dissociation of ions

Water, as you probably know, is highly polar and has a very high dielectric constant. When ionic compounds are added to the water, the electrostatic force of attraction between the ions get very weak and hence will result in dissociation of the compound.

The percentage of dissociation of a compound depends on various factors such as solvent, strength of ionic bond, etc.

$\ce{HCl}$ is a polar molecule and hence it dissociates into its constituent ions, namely, $\ce{H+}$ and $\ce{Cl-}$ ions.

Your initial question "what is the pH of HCl" is not quite right. More about it in the next section.



What is pH?$\space$ Can pH be negative?

pH by definition is a measure of hydrogen ion concentration. 

$\mathrm{pH} = -\log[\ce{H+}]$ where $[\ce{H+}]$ denotes the active hydrogen ion concentration.

Hence, $\mathrm{pH}$ of $\ce{HCl}$ in an arbitary context won't make any sense since the $\mathrm{pH}$ of $\ce{HCl}$ would depend on its concentration.

The $\mathrm{pH}$ of a substance can be negative. $10\ \mathrm M$ solution of $\ce{HCl}$ would have a $\mathrm{pH}$ of $-1$.

The stronger the acid, the smaller is the value of $\mathrm{pH}$. $\ce{HCl}$ is a strong acid because it ungergoes almost 100 % dissociation.



Theory of acids and bases and their relation with pH

The theory of acids which you are refering to were developed to classify acids and bases rather not to measure the strength of the acids and bases.

However, one can arrive at the strength of the acid/base according to the theory by logical reasoning. For example, if someone were to ask you which one of the two compounds is an Lewis acid, you would investigate both the molecules and find out which one has a higher tendency to accept electrons to find the stronger acid.

Therefore, the theory of acids proposed by Arrhenius and Brønsted–Lowry are in no way related to $\mathrm{pH}$. 

pH on the other hand, is a measure of strength of an acid and is indepdent of the above theories.

It is quite easy to compare $\mathrm{pH}$ with Arrhenius/Brønsted–Lowry theory of acids since according to the theory, the molecule which is willing to donate free $\ce{H+}$ ions will be considered an acid. A claim that higher the concentration of $\ce{H+}$ will be a stronger acid is reasonable, understandable and acceptable.

Bonus:
In case of bases, we have a strength measurement scale similar to the pH. We make use of hydroxide ion concentration in place of hydrogen ion concentration to find the strength of the base. We call it $\mathrm{pOH}$.

These two are related by the following formula when the acid/base are dissolved in water at room temperature.

$14 = \mathrm{pH} + \mathrm{pOH}$