I've never heard of Skin, but I can try to give you some tips on writing for context in general.
Namely: Think outside of the box.
That means not opening any study guides yet. That means forming your own opinions of characters, ideas, concepts before you start to let others' opinions filter into your own writing. Your context piece will sound more authentic and fresh if you pour your own ideas into it first. The beauty of English is that provided you can back up your thinking, you can never be wrong!
Don't get me wrong, your teachers' ideas and study guides are BRILLIANT, but I'd strongly, strongly advise to let their ideas filter their way into your mind AFTER you've formed your own opinions about stuff.
Now that's out the way..
Let's go back a step. Let's look at the sheer basics of context. So don't fret too much, you've got plenty of time to perfect this. So let's start getting things straight:
The context section of the course gives you quite a few options in terms of presenting your work. So from now on, figure out which style you are best suited to. By all means, experiment with different styles and talk to your teacher about playing to your strengths. Do you enjoy imaginative writing, and are you good at it? Do you like writing speeches? Can you give a convincing argument? Are you comfortable with writing in a different persona, in a different era? Do you like narratives or would you prefer to write in a stream of consciousness? Are you better at laying out facts? Can you use anecdotes well? Do you like using case studies or current events to flesh out a story or an argument? Once you can answer these questions, you will be better equipped to make that decision about whether you'll be focusing on an imaginative, persuasive or expository piece of context writing. And by all means, you can make a happy hybrid! You can persuade in an imaginative context using a speech. You can select from a plethora of text-types, from blog posts to an epilogue chapter or extended ending of your novel or film that you are studying. The possibilities are endless! (Almost - Poetry however is to be avoided as it is not a piece of prose). Keep in mind that whatever writing choices you make (present tense, writing in a character's voice, etc) they need to be consistent. This is an easy mistake to make (and to fix!) so don't overlook it!
So once you've figured out all of this, you're pretty much half-way there!
Now, I'll try my best to answer your questions.
How to study for context and taking notes:
I never wrote notes. Seriously. I just sat there in class, absorbing shiz. This approach seemed to work for me. I listened to ideas, then wrote stacks of practice essays, but never a note on context. Personally, you don't have to make your hand fall off from writing notes about the text you're studying. Some students in my class did, but I found that it didn't work for me. Knowing your text is the crucial bit, so whether that means writing out chunks of quotes or paragraphs on paper helps is up to you. I liked watching film adaptions of my books because I'm shocking at remembering quotes on paper unless they come to life before me on a big screen. So if you've got a film, watch it countless times. Scribble down quotes if you like. Discuss the characters and themes and the plot with friends and peers and ALL English teachers. Get involved. Actually immerse yourself in the text, debate the happenings in the film with peers as though they were ACTUALLY real-life people.
I personally just went with "ideas" from the text and that was the basis or inspiration for my context pieces. My personal approach was to just THINK about what I was going to do with the context component of the course and that was really ALL the preparation that I needed. So I would think about a particular character I liked in my text and take the text into that person's perspective to make it a more interesting piece. I would mention significant events or symbols used in the context to make sure the examiner or marker knew that I was making connections with the text rather than just waffling on about some sort of narrative that's off-topic. I would mentally prepare by thinking about how I wanted to start my piece. I'd consider what aspects of the characters I wanted to focus on, how I would link each paragraph, how the connections with the specific context prompt, the text and the context itself are shown in every single paragraph, etc. This might've only taken me an hour, the night before a SAC. I'd jot down ideas on paper to jog my memory. Plans were crucial too. Once you've got an idea of what to write about and you've got some sort of direction, the writing flows from then on.
Then there's the technical side to context. Allow time for planning and proof-reading. Work to time. If you can't fit in enough time for context writing, then start with open notes and open time, then work with open notes and closed time until you can finally have closed time and no notes! Check your accuracy (grammar, expression, spelling) after each paragraph you write rather than having to edit a hectic slab at the end of your piece when you feel more rushed.
Hope that's of some use to you.
Cheers