It only counts steps for each individual day, and watts are sent back after every "stroll". As far as Pokemon available for catching, it splits them into three groups, common, uncommon, and rare. There's 6 pokemon available per course, 2 for each group. Every "stroll" it pulls one pokemon from each group for you to catch. Naturally, in this case, Fly pikachu, and surf pikachu are both in group C. So every time you take a walk on the course you have a chance for one or the other, but not both, and there's no way to tell until you transfer them back.
10,000 steps really isn't that much. On days when I work, and have class I average about 20k. Of course, not everybody may have the same oppurtunities to walk, in that case there's dozens of ways to cheat the walker.