Great topic, I think. I've always been fascinated by the process of creating things, whether it be a painting or a sketch or a story, poem, etc. I could watch people work literally for hours.
I have only been writing for about four years now, and only three in earnest; so I guess I don't know much but I'll tell you what I do have.
When I write, I rarely have drafts. I write poetry for the most part, but I'll go into short stories or essays if I haven't been able to get the creative juices flowing for a while. For me, the change in "scenery," is refreshing, and I feel that it gives me a chance to address the same issues, (or different ones,) using different techniques in say, grammar and syntax.
Instead of drafts, I edit as I go; sometimes this means I will go back and change a line, or a word, or punctuation mark, at the very end, after I've surveyed the whole work. Usually I simply edit something immediately; when it works, I know it works. When it doesn't work, I know it and change it right away.
I could never write in public, I feel very self-conscious when I'm around people, (I have a lot of friends, but I've known them for years so it isn't so bad when I'm with them,) and when I write, I have a lot of almost pedantic habits because I have OCD. I have to have the paper just right, the pen has to be held a certain way, I have to shift around in my seat; and when not writing poetry I'll often get up and pace to help me think.
I don't mind being outside though, some of my "best," work, (as I said, I'm still a wee lad in the world of writing,) has been written in a simple lawn chair that I've had for probably a decade on the porch out back. It's a pretty calm neighborhood, a lot of elderly folks and the only real bother are birds that never shut up. They'll yell all day, ugh!
I definitely prefer to write in my bedroom, in a corner at my desk.
I like the quiet of night, and I'm a night person, usually sleeping in the day and writing at night, (I'm 17, and I thankfully don't have to work right now, so I can afford to be lazy, heh,) but again, some of my best work is done in the day.
As for music, I can write in silence, but even then, there is often music "playing," in my head. I'm not crazy, but I mean I'll get songs stuck in there. It kind of helps if I want to hear a certain song, because I can get a song stuck on purpose.
I prefer indie-type or anthemic music, or older stuff. The Moldy Peaches, Arcade Fire, Feist, Broken Social Scene, Leonard Cohen, and Bob Dylan are frequent plays. I don't need them to write, but they help me. I like to get lost in a song, whether by just going with its' flow or by putting myself in its' story.
I don't really see my poems as living things, but rather as photographs. I view them as a "snapshot," of say, a scene or what have you. If I'm writing something that is long, or a short story or essay, then they definitely grow.
When they do "grow," it isn't in a linear fashion. I have a really branching idea of what is going to happen, or what I will say, and this creates problems later on when I have to figure out where to put everything. It is challenging work, and I thoroughly enjoy viewing the possibilities. I think it might be akin to raising a child, but what with my age, I wouldn't know.
I cannot write on the computer. I hate even copying things I've written by hand.
I'm new to fountain pens. Actually, I've only ever written with other peoples'. I just ordered my first pen and ink, Lamy Safari and Aurora Black. I went with fountain pens because I liked how they flow, or glide, across the page. I need to be able to put ink ONTO the page, rather than INTO the page as with traditional pens, even roller-balls.
If I can write quickly, with a smooth pen, then it helps me understand my poem as a snapshot, as a fleeting, if, (hopefully!) timeless, picture of life.
Sorry for going on for so long and for any grammatical/orthographic errors!