The answers to your questions are more or less based on the code of your other project, not on CodeIgniter, though I can say that for #1, there's almost no benefit to putting something in the root folder of your CodeIgniter project.
In most cases, if I want to integrate an external PHP library or application with CI without doing some heavy modification of the library/application, I put it in the /application/third_party/ directory and write a library (in /application/libraries/) to interface my CI application to the external library/application. The exception would be if I could auto-load the library with Composer, in which case I would do that instead of putting it in the /application/third_party directory.
In some cases, you could put the library/application in your /application/libraries directory. The loader is pretty forgiving when you load libraries, but there are certainly cases in which this can cause more problems than it's worth.
#2 and 3 are not likely to be answerable without more information about the database resource and how you expect to access it. Additionally, a "vanilla PHP" application, especially from several years ago, could mean a lot of different things. The easiest way to get it to work with your CRM would probably be to refactor it into a CodeIgniter library or controller, or setup a controller and/or library to interface with it. Once you have something like that working, you could take your time refactoring the rest of it into your CI application.
