These alterations look totally valid to me and I see no reason why you should worry about them.

If you want to have the system send you a simple message that says "Someone has placed on order" you could hardcode something like this in there:

$email_text = "This order is to inform you that an order has been placed on www.something.com

To view the order, please log in to www.something.com/admin.or.whatever/
";
zen_mail('', '[Your email address]', 'Order placed', $email_text, STORE_NAME, EMAIL_FROM, '', '');

I don't know what the last two variables for the zen_mail() function are supposed to be, so I just put them as '' - this may cause a problem, so if it doesn't work, mess around with it if you feel like.

Best of luck!