Automate PDF actions
The answer to your second question might lead you directly to a solution to the first.

You'll want a tool that edits PDF files to append docments (or conversely, split them up). I use PDFPen for the job, but there are others that do less but might meet your needs.

Here is an article on using Hazel to script PDFPen as well as documentation on how PDFPen is scriptable in general. There is a Pro version of the app for a higher cost, so you might see if you need the extra features, but the normal version seems to meet your needs well enough.

Many helpful PDFPen example scripts can be found after you install the software in your user library: 

~/Library/Application Support/PDFpen/Scripts


Opening them in the AppleScript Editor is a great way to learn more.