1.) Yes, you can remove the disc after launching the homebrew, as the PS2 isn't reading off of the disc anymore.
2.) Kernelloader is the homebrew that allows you to load Linux so that's pretty cool that you can run an OS on your PS2, you probably know about SMS cause you mentioned it in your last post. PS2ESDL is like Open PS2 Loader except it only loads from USB and also loads a bit faster. Hmm, there is a bunch of different emulators also, such as PS2PSXe which lets you play PS1 games off of USB, Network, and HDD. That's pretty much it, what more could you want?
3.) I'm not entirely sure because I have no experience with modchips but I have no idea why it wouldn't work. You could research more on the web if you really want to find out.
I'm going to do tutorials for Open PS2 Loader, PS2PSXe, hopefully Linux, and also how to use ESR so check back if you need any help on these.