Short answer - No.

Long answer - It would take a lot of effort, generally more than it would take to duplicate the desired functionality in one or the other.

It depends on what you need each for which way I'd suggest going.

They both have different databases, meaning they will require their own user information, which [using the default in either] will not propagate to the other. That's the major issue.
Then to get any user related information you will have to store some identifier the other system knows to pass back and forth, and validate it...

I wouldn't recommend combining - I'd recommend using one or the other and migrating as soon as possible. A custom module to show reports from the old database [if needed] isn't too hard - I think the DNN Reports module could do that.

It depends on what you mean by work together.  If you just want the two sites to "appear" as a single site, then that is completely possible using virtual applications in IIS.  Also, it is completely possible for PHP code to read/write to the DNN database.  And of course if you use web-services and a little bit of AJAX code, you can make any two web applications work together.