1.) First off, what is the correct terminology for an array created on the end of the name element of an input tag in a form?
"Oftimes Confusing PHPism"
As far as JavaScript is concerned a bunch of form controls with the same name are just a bunch of form controls with the same name, and form controls with names that include square brackets are just form controls with names that include square brackets.
The PHP naming convention for form controls with the same name is sometimes useful (when you have a number of groups of controls so you can do things like this:
<input name="name[1]">
<input name="email[1]">
<input name="sex[1]" type="radio" value="m">
<input name="sex[1]" type="radio" value="f">
<input name="name[2]">
<input name="email[2]">
<input name="sex[2]" type="radio" value="m">
<input name="sex[2]" type="radio" value="f">
) but does confuse some people. Some other languages have adopted the convention since this was originally written, but generally only as an optional feature. For example, via this module for JavaScript.
2.) How do I get the information from that array with JavaScript?
It is still just a matter of getting the property with the same name as the form control from elements. The trick is that since the name of the form controls includes square brackets, you can't use dot notation and have to use square bracket notation just like any other JavaScript property name that includes special characters.
Since you have multiple elements with that name, it will be a collection rather then a single control, so you can loop over it with a standard for loop that makes use of its length property.
var myForm = document.forms.id_of_form;
var myControls = myForm.elements['p_id[]'];
for (var i = 0; i < myControls.length; i++) {
var aControl = myControls[i];
}