Hi Ashley,
The process of making a PDF entirely 'read only' is called 'Flattening'. I assume that you want to flatten the form after one of your coworkers has filled it in. Adobe has some very extensive server-side software that is capable of handling everything that you are asking for, but the price tag is very steep.
A free work around is to use a virtual printer to 'print' to a new file. I personally use CutePDF which is free and very easy to use. You install it as a printer on your computer, and then 'File ---> Print', select 'Cute PDF' as your printer, and then hit print. Instead of physically being printed, CutePDF will ask you to 'save as.' the new file is a pdf file that is exactly like the one you printed, but it can't be edited.
I hope this helps! If you have any other questions, just ask... I'll keep an eye on this thread.
- Scott