1. Is it necessary to always open Google Chrome from terminal, and 2. Must the terminal screen be kept open for Google Chrome to keep working?

No. Chrome should show up in the applications of menu of most desktop environments. You can also launch it from a simple run prompt in most environments by pressing Alt-F2, and then entering google-Chrome in the box. Normally, closing the terminal would close Chrome (or most applications launched from it). If you launch google-chrome as a background process (using the command "google-chrome &") and then disown the process (running "disown #", where # is the PID of the process), you can close the terminal and leave Chrome running. Alternatively, launch Chrome with nohup ("nohup google-chrome") and then close the terminal.