[Shamun]

If you need to use your own functions, then you should make a new folder under /modules/ in the root dir. This will keep all your stuff in one place. I would do something like
/modules/wp_integration/
Then make your php file in there with your functions.

Then you can make an init.php file in there with your functions or to make it logical, you can make init.php and then include your funcs.php file from there. X-cart auto-loads any init.php in a module directory.

As for your internal errors, I'm fairly certain it's because of conflicting function names or session problems. Fixing the first is not good as it will pretty much render the application you changed unupgradable. Fixing the second is possible, but requires alot of work.

If all you need is a design from WP, then make it in x-cart. Integrating it is much harder. If you need certain elements, make some functions to work on the WP db. Doing a full-on integration is more than a 10 hour job.