unless you, by chance, have already own the necessary materials needed to hack the ps2, it's not possible to hack it without procuring some costs.
Also, it is indeed possible to play ps2 "roms" (actually iso files) from an external HDD, however it is not recommended, because PS2 is limited with USB 1.1 port, so slowdowns will occur.
Of course, all of these require that you first hack your PS2 (which involves putting a program called FMCB into your memory card), which require you to have either:
a. a cheatdisk such as AR max, codebreaker, gameshark, etc which allow for usb drive to memory card write access, OR
b. a swap magic retail disc, OR
c. a memor32 card, OR
d. a retail HDL/HDA disc, OR
e. a retail copy of 007 Agent under fire or 007 from Russia with love.
The best way to play ps2 iso in your fat ps2 is to uses an internal IDE HDD which requires a PS2 network adapter. The program required for this is OPL or HDL.
You can also burn the iso and run it through a program called ESR. The quality of the blank DVD is very important, as is how you burn the iso.
You can also run it through a network or USB drive, but once again, slow downs will occur using these methods.
OPL, HDL, and ESR is included in FMCB noobie package.