I took these pictures last February on a road in Olympic National Park.
1. What species?
Looks like people did pretty well recognizing characteristics of felines. They are (a bit) asymmetrical, front of the heel pad is bi-lobed back of it is tri-lobed (when the detail shows up), the negative space is small and does not have an X shape, also no claws showing.
I'm pretty sure however that this is a large bobcat rather than a small cougar. It would be very small for a cougar and we didn't see any tracks around suggesting it was with its mother. I'm not really sure how to differentiate small cougar and large bobcat from foot morphology. I would be quite interested in hearing if anybody knows some characteristics to look for there.
2. Which foot is the ruler next to?
It is the right hind. Hind feet in cats are generally narrower (particularly the heel pad) than their fronts, this gives them a bit more of an oblong look where as their fronts tend to be more circular. This individual track looks even longer because it seems to have scuffed a bit adding length to the rear of the track.
It is fairly easy to see here that it is on the right side of the body, but if that were not so clear you can also use the fact that cats (true also for many other animals) have a leading toe. For cats it is toe 3. Counting from the inside of the foot, toe 1 generally does not register (look at a cat's foot and you can see they have a toe a little ways back on the inside), toe 2 is the innermost that reliably registers and toe 3 is the second from the inside of the toes that show up. In the track in question it is not especially obvious, but I think many of the other tracks in the trail do show the leading toe more clearly.
3. What is the gait?
This is an overstep walk. Recognizing it is a walk is a good start. And knowing which feet are which shows it is an overstep.
I had a fair bit of trouble with gaits starting out. One thing that helped me was realizing that most animals have characteristic gaits they use. When I was taking the cybertracker evaluation I had missed a couple of coyote gait questions that happened to be overstep walks. The evaluator told us that he sees coyotes in an overstep walk so often that if he sees a track pattern like that he starts from the thought of it being an overstep walk and tries to prove it wrong. Of course, knowing what gaits animals use comes from experience and study (and it's handy if somebody experienced shares their knowledge with you as the evaluator did with me). In my experience, overstep walks are not unusual, but understep walks are.
Bonus: What sex?
I'm not real good at sexing felines from their tracks yet, but apparently it can be done. Size is definitely a good clue and since it is large for a bobcat, that points towards male. Other things to consider are the robustness of the track. From what I understand female felines tend to have "daintier" toes and heel pads which will leave more space between them. Males have beefier feet which tend to have less space between the toes and between the toes and heel pad.
It really is a relative evaluation, but these tracks look pretty robust and are definitely large, so I think it is a male (and that was the general evaluation of the tracking group I was with as well).