Form Validation (JQuery)
First of all, you shouldn't use $('.submit').click() but $('#myForm').submit() as you will be able to submit forms by pressing enter too.
To check if a string is a number, use !isNan(string) (see this answer for more information).
Email regex are difficult things. Just check if there is someting before the @ (with .+?) and if there is something after the @ (again with .+?) and if that last part contains a . and a couple of characters (from 2 to 6)
It would make the function a lot easier if you put all specific code outside it. E.g:


    validateForm({
        '#nameInput': {
            'valid': function (value) {
                return /^[a-z]+$/i.test(value);
            },
            'label': '#nameLabel',
            'messages': {
                'empty': 'Please enter your name',
                'invalid': 'Letters only',
            },
        },
        '#companyInput': {
            'label': '#companyLabel',
            'messages': {
                'empty': 'Please enter your company',
            },
        },
        // ...
    });