How do I roll or wrap up pasta into a log-like shape for presentation?
Do they use some kind of tool to wrap the pasta around?
The answer is in your third picture -- chopsticks.
Grab the bunch with the chopsticks, twirl it around, then slide the chopsticks out.
you could use the chopsticks to twirl your spaghetti like in this video Twirl Spaghetti with chopsticks