I have my Arch Linux installation pen drive and I'm wondering if I have to install it on other disk or flash drive. Can I use this installation pen as there was a system and install X11 and all packages I want there?
No. What you have is (most likely) an installation disk, not a live system with persistence (which seems to be what you want). For some instructions on how to set up a live system with persistence, see the Arch Linux wiki here. However, that page says it's out of date, and doesn't point one to up to date instructions. I am a Debian Live user myself (as a live system with persistence on a pen drive) so I don't have more details. Incidentally, if you are not committed to Arch, the Debian Live system is the most reliable, consistent and flexible that I've found for running Linux off of a pen drive.