All the stuff that you see in this video is real, but it's accessible only through cheat codes (except for jumping bug, that can be found only on Kingdom Hearts I US Version - SLUS_20370).
INSTALL MENU: can be enabled with a cheat or if a proper formatted HDD is found. Old PS2 models supports external hard drive and, in japan, was used to install games in order to improve loading times. In US and EU versions you are not supposed to use it, infact the texts at install menu are unreadable because the game try to display japanese characters with our alphabet but without success. If you want other infromations about the Install option, please visit this link http://bungiefan.tripod.com/psbbn_01.html
LONG HP Bar: I downloaded a savegame from internet in order to show you that glitched area. I'm european and, honestly, I decided to not play entirely the game only to test 3 minutes of a thing. The save was previously modified with cheat codes for sure, It wasn't modified by me and I'm sorry if it cause that terrible and annoying noise.
THE JUMP GLITCH at 1:40 works only on early version (US and probably JAP non-FM). It was confirmed from some people here in comments that it doesn't work on EU and 1.5 versions (NO HD BUGS T_T).
BAHAMUT SUMMON is selectable, but doing that will freeze the game. Text and menu entry was left there, but there is no data for the summon. I searched through the game files but I cannot locate it.
It was 2007 the year that I recorded this video from my PS2 and I didn't have the tools, a powerful pc and the knowledge to make good and professional videos. I was only a child :)