Long format answers:
Developing good written communication to lay out cogent scientific arguments is an essential part of the Earth Sciences degree, and a very valuable skill more generally beyond academia. Feedback on supervision work provides the key opportunity for you to hone your writing skills. There is also a great article on the science of scientific writing by George Gopen and Judith Swan, which you can find online here, or a pdf here.
Presentation: I would consider handwriting your essays and hand drawing any figures/graphs that you want to include. The reason for this is that the examination at the end of the year will (for most people) involve handwriting your essays within a time limit, so it is important to maintain practice at this during the year.
Length: In the 1A exam at the end of the year you have ~36 minutes per essay. For most people this translate to 2-4 sides of text and figures. You should expect to cover about this many sides of A4 with text and figures in your supervision essays, although with researching from your lecture notes and from recommended reading, it will take longer to write.
Again, I would recommend the doing the work handwritten. In the case of calculation work, this is mainly because it would be inordinately awkward to appropriately typeset the maths describing your workings.
Thin sections and rock descriptions:
I have produced a short guide for thin section and hand specimen descriptions that goes into more detail. In brief, it is best practice to make the annotated drawing on one blank page of A4 and then further written observations and inferences on a second page. Use colour, shading, differing line weights etc., to best communicate the optical differences between minerals.
Where and when to hand work in
Please hand your work into my pigeon hole (or email it) in my Earth Sciences Department pigeon hole the 24hr before the supervision.