Hi Mai
Welcome to the forum!
There is a run called Les Marrades that goes to just by the Patagonia. It's actually had a facelift over the summer, plus snow cannons added, so weather permitting it should be open, and this season with the added snow making it should be in better condition throughout the season. Alternatively, you can just ride the chairlift back down either with your skis on or off.
The walk down to town takes about 10 - 12 minutes, and maybe a little longer to walk back up!
The times of your lessons depends on your tour operator. In previous seasons Neilson have had afternoon slots which are Monday 12-2 & 4-5, then Tuesday - Friday 12-3. Beginners and intermediates are at the same time. If you've not already booked you lessons, from October you'll be able to book on here and choose either morning or afternoon time slots.
There is a free bus that goes from Arinsal to Arcalis twice daily. It goes from just by the Patagonia, also stopping in the village centre. Also, last year Neilson ran an organised trip where a rep goes on the coach with you and lunch is included. Your holiday rep will be able to get you booked on that at your welcome meeting.
If you have any more questions get them posted on here and we'll try our best to help!
Steve