How FUN!!
Do you have your own horse at home to practice your newly acquired groundwork skills with? If you do, watch for the small details while you work with him/her (or if not, watch your lesson horse closely). Watch for things like licking lips/chewing, yawning, ear movements, very slight body movements, noises, snorts, or deep breaths. Your instructor will be able to interpret this body language for you if you don't already know what they mean. You'll be amazed and what your horse tells you when you're actually listening...or, well, looking.
I recently started doing more groundwork with my horse using the Parelli system. Of course, this DVD system will be nothing compared to your one-on-one instructor training! I'm jealous! Anyways, on my 2nd day with Parelli, my horse was doing well, then after about 45 minutes, he started yawning repeatedly! I just thought he must be tired and finished up quickly, then put him to bed. That night I watched the next DVD in my Parelli set and Linda Parelli mentioned that often a horse will be riled up on adrenaline and then after you do your groundwork games, he'll calm down. She said, as he's coming off the adrenaline, he'll often yawn! Wow! I had no idea what this meant when my horse was yawning, but I had noticed the sign.
My advice to you in your new lessons: ask LOTS of questions and remember, slow and consistent always wins! If you ask your lesson horse to do something, and he doesn't do it, it's probably because you asked wrong! =) Ask your instructor (who speaks your language

) to ensure that you asked the horse properly to do what you wanted. Ask the horse consistently in the right way and your horse will get it soon enough (as a lesson horse, he probably will give his best try very quickly...he's used to people not asking *quite* right).
Sorry, I don't have much experience with Paso Finos to give you any advice on them. But, if you like the horse they team you with, I'd ask to ALWAYS get to work with the same horse. You'll develop a better bond and be able to go further in your groundwork together. Otherwise, each lesson you'll just be meeting new horses and playing the "who's alpha" game each lesson.
Have fun and wear comfy shoes!