I have visited the park and I have watched this camera many times before. Yellowstone is about 200 miles south of me.

It is steam you are seeing, not smoke. The temperature of the water coming out of those geysers is well over 200*F. The ambient air temperature is currently 36*F so you see lots of steam. Even when it is 70-80*F you see lots of steam.

You are watching Old Faithful. It is called Old Faithful because it faithfully goes off, roughly, every 90 minutes. Seeing multiple geysers steaming at the same time in this area is not unusual.

There are geysers throughout the park so you will see steam rise in the background/tree line.

The camera you are watching has always panned back and forth. During daylight hours there is someone operating it to provide the best view for people watching and during tourist season the operator can keep an eye out to make sure tourists don't venture off the designated paths and put themselves in more danger than they are already in standing in the caldera of the largest volcano in the world.

The camera is mounted to a tree and does sway back and forth. You should see how much it sways when it is really windy.