The different widths for the charging adapter plug should be the difference between the older Magsafe, and the newer Magsafe 2.
To change the login password -- Try booting to your recovery system, by holding Command-R, while booting. You should see a menu screen, with some choices.
Go to the Utilities menu, and choose Terminal.
You can then type "resetpassword" (without the quotes)
press Enter, then follow the on-screen prompts to set a new login password.