For holding down the wires, regular old hot glue is safe. However it is a good idea to keep the glue off any chips on the mobo as the glue can actually work as an insulator and possibly cause the chip on the mobo to over heat. As for how to hold the DUO down to the mobo, the chip will come with double sided tape on the back of it already, so you’re set there.
As for the different soldering methods, the best advice I can give you is to
not learn how to solder on the PS2. Find and old CD player, phone, or whatever that has small points like that of the PS2's mobo and practice A LOT. I could tell you over and over again the different ways to solder but until you have actually tried it; it wont really matter.
Do a search and you will find many good posts on different methods, but if your to lazy to do a search on your own here is a thread that has some good advice.
http://www.fileforums.com/showthread...threadid=58172