How do I select the parent form based on which submit button is clicked?

You can select the form like this:

$("#submit").click(function(){
    var form = $(this).parents('form:first');
    ...
});

However, it is generally better to attach the event to the submit event of the form itself, as it will trigger even when submitting by pressing the enter key from one of the fields:

$('form#myform1').submit(function(e){
     e.preventDefault(); //Prevent the normal submission action
     var form = this;
     // ... Handle form submission
});

To select fields inside the form, use the form context. For example:

$("input[name="somename"]",form).val();