Hi Amir,
Sorry to be so slow to respond. Currently I am only able to work on Moodle stuff for a couple of hours each morning. Other projects keep me out of the house and very busy the rest of the day.
From your previous description of starting out in your new fastassign, then winding up back in a web page of the regular assignment plugin, I think the one step you may have missed, is to go through the code files, looking for links to other files that belong in the plugin.
For instance, when you go to an assignment, you generally start in the view.php file. Open that file from your fastassignment plugin in an editor such as Notepad++, and do a Find > Count search for ".php" (without the quotes). In view.php you should get a count of three. The first one in line 25, doesn't matter. The second you have to verify that, /mod/assign/locallib.php, has been changed to /mod/fastassign/locallib.php. Then down in line 44, /mod/assign/view.php has been changed to, /mod/fastassign/view.php. Then go repeat for every file in every folder of your plugin. When doing these searches, make sure that Match Case is OFF, and Wrap around is ON. Otherwise it is easy for a search and replace operation to miss some of the things you are looking for.
You need to go through every file and verify because it is so easy to accidentally miss one occurrence, that breaks everything.
Another thing to check is in lib.php and locallib.php. Many times due to the way Moodle works, it will not let you use a function name that is the same in both assign and fastassign. Every assign function in local.php has assign in the name, so those all have to be checked and assign changed to fastassign. The functions in locallib.php are likely culprits for causing problems, as they do not currently have assign as part of their names and a search and replace would not do anything to them. So, try to run the parts of your new fastassign, to see if they are what caused your previous errors.
When trying to run your new version of the plugin, set debugging to developer, and try every part of the new plugin. If you get any problems, they HAVE to be fixed. Post the debug info, if you still have problems.