Looking at the mail system, those pages have several blocks on them. For example, go to the inbox, click on a mail message and it opens it in a page with the message and the actions block and to the right is an archive block with a history of messages From the sender and you can switch it to To the sender.
Now, it you just want the pages to open in a pop-up, you can do that with javascript and change the links to include an on-click; but that is going to open the entire page, header and all. You are not being specific enough to get an answer. If you just want the message from the inbox to open in a pop-up so you can read it, then that is different from opening the entire page in a pop-up. And you still need a way to open the compose reply to reply to the message.
You would have to sit down and write a detailed report of what you want done. This is where a lot of projects go wrong, the person says they want one thing when they really want something else, the developer does what the person asks but it is not what the person really wanted. When I do such work, my first job is to talk with the person back and forth to map out what they really want done. You need to think about how you want the mail system to work; and you need to write a detail report on that. You map out how the interface should work. For example, I click on inbox, I get a list of the messages in my inbox, I click on a message I want to read; it opens in a pop-up or modal window (a modal window, by the way, is one that you can not click outside the window). The pop-up window will contain a reply button. If I click on the reply button, the pop-up window closes and takes me to a compose reply page; or you may want that in a pop-up window as well. These are the kinds of things you will need to map out in your project request.
Now, since this project probably means a rewrite of the entire mail system I doubt if anyone will take the project on. Plus, it could take months to rewrite it and get it working and remove bugs. You would need to write up a contract; Boonex will not help if the developer takes your money and runs; you will need to do that in the court system. Break the project up into sections, detailing what is what, how payments will be made, what benchmarks must be reached, etc.