Cool idea! I love hearing about what other people do.
1. How do you choose pictures, textures, font, text brushes etc. etc. etc.
Usually I'm inspired to make graphics after watching a movie or show. For example, I just watched
Under the Greenwood Tree so I have a feeling I'll be making a lot of period films graphics. I have a huuuuge bookmarked screencap collection, so I just go through until I get the pictures I want. At the moment I'm more into icons than anything else (I blame livejournal) so I look for pictures with interesting compositions, colors, or crops. I'm hopeless at text (probably one reason I like icons) and don't often use textures or brushes. I have a few saved, but mostly just work with color.
2. Does it differ if you're doing an avatar vs. a banner? Or a background or a blend?
I guess I should've read through the questions before I started answering.

Yeah. With banners, I tend to look for pictures from scenes so that the coloring will go together and I have text ready-made. If I don't make a scene banner, I usually look for HQ pictures and work from that. Wallpapers are 99% of the time HQ pictures, and I tend to arrange them in the same way. It's just collecting and colors.
3. What order do you make them in? Picture-texture/brushes-text? Or what?
Picture, color, color, text.
4. How do you choose your text? Song lyrics, quotes, stuff you just come up with?
Usually quotes. I have a list of some songs that have good lyrics, and if I come across things that just fit with certain themes, I keep a note of it and use those. I can't just come up with things off the top of my head. I fail.
5. Do you make, and re-make graphics until they're perfect? Or just make one and figure that's the way it's supposed to be?
Generally I just make one (banner). If I like the pictures, I may do three or four different versions and see how they turn out. I usually keep them all, though. With icons I like to move one picture around a lot to see what sort of cropping I can get on it, or put text/no text, brushes/no brushes, gradients, etc.