Lots of great advice here. A couple of things I'd add:
1. Totally agree that when in doubt, ask. If the instructor makes you feel stupid, they are not the right instructor, especially for a beginner.
2. For cleaning the face, some people may use a baby wipe to gently wipe away the grime. But I would definitely ask the instructor about their preferences.
3. As far as the various "school figures" it sounds like you're being asked to do, my guess is that maybe you were introduced to:
a. Figure 8s- like it sounds, making a big number 8 with two 20 meter circles stacked "on top of each other," with one circle ridden in each direction, changing direction in the middle. Looks like this:
b. Serpentines- moving across the arena in a 2, 3, or 4 loop pattern that looks like this:
More info here
c. Changing direction "across x" or "across the diagonal"
If you dropped a pin down in the exact center of the arena, you'd be at "x," even though that letter isn't posted in the arena. If you change across X, you pass through that dead center marker, often using the "diagonal" that has been explained to you (K to M or F to H).
4. Changing direction down the center line- you use a straight line through the middle of the arena (e.g., C to X to A) to change direction
Here's another visual representation of the school figures above (which I would think of as the most common for new beginners) plus more- this figure shows how things get more interesting as a rider starts to gain more control of their own body, as well as the horse's, to execute more complex turns and changes.
I also really like this little book
. Even though it's written for instructors of kids, I liked it for ideas for adult beginners too- it's not babyish and it basically covers all of the figures in the image above with an explanation of why you're doing them. I'd suggest grabbing a copy if you want it handy to reference- you can literally get a used copy on Amazon for $2. This one
is good too, with lots of pictures and clearly written explanations.
Most importantly, have fun and enjoy that horse time