1. No, you do not have to buy a network adapter with the slim PS2 (but that will not matter).
2. Alright, I am going to try to answer you with my (apparently) limited knowledge:
You do not connect a USD HDD to the network adapter. You need to use an internal IDE drive. HDloader will not run a game from a USB HDD.
Also, you can not install an internal HDD on a slim PS2. Sony lost interest after HDloader was made (I wonder why ?).
However, there is some homebrew called USBadvance/USBExtreme that will load form the USB port at the front of the console. You can use either a Flash/Jump/Pen Drive, an external HDD, or an internal HDD with an external USB Enclosure.
But like Zorlon said earlier, it uses USB 1.1, so running games will load very slowly with limited compatibility. Check out this Compatibility List
My advice:
If you are getting a Slim (SCPH-70000), use discs. If you are getting a 'fat' (SCPH-30000), you may want to consider getting an internal HDD.
Um... Why? You still need a way to install it on your memory card/run custom .elfs. Are you going to buy the HDLoader disk? I would not recommend it, there is the fore-mentioned free service on this site, and there is this guide:
http://www.epforums.org/showthread.p...e-to-SWAPMAGIC