EDIT: Just in case you misunderstand, I used the term "habit" and the like more than just a few times, but it's not a common or official term by any means. I just used them to better explain things. Also, sorry for choppy/repetitive language if there is any; was half-asleep from just waking up when I wrote this lol.
Couldn't exactly remember what was covered in the vid so I had to rewatch it aha.
In short, reading your opponent is basically as you said in the OP; it's predicting what your opponent is about to do. The things the vid covers are methods of improving how effectively you can predict their movements, and how you can punish them for it. They're just good examples you should keep in mind.
A person's "style", as he puts it, refers to their habits. It's bad to have habits; it means that they follow a certain pattern that can be observed and punished, just like how he pointed out that Fox rolls away after F-throw and punished by running forwards and attacking the next time.
Reads at low-mid level of play are often not very frequent; most people don't naturally think to look out for and notice these things, so when you hear friends talking about reads, they're probably referring to how they consider their opponents available options and punish what they think would be the most effective one. That differs from reading "styles", in that it doesn't necessarily consider the opponent's habits, but usually just guessing out of whichever options they're limited to.
As long as you don't punish habits in the exact same way every time, they probably won't notice they're being read on that level, unless they know to look out for habit-reads. So, if you mixup what you use to punish a given habit ever so often, then yes - they'll probably keep repeating it. That's what the guy meant by assuming they're always stupid instead of smart. Even if they do catch on to being read, it'll often work due to habits being hard to break. Muscle-memory reactions can be a ***** aha.
That's right. You can either preemptively approach their shield and use quick attacks like jabs (just tapping the A button) or sometimes tilts. That way, if they planned to grab you, you might catch them with a jab hit before they can grab. If they planned to spot dodge or roll away, you can have enough time to follow-up and grab/attack wherever they end up before they can move again. If you feel like they were planning on staying in shield longer (e.g. You notice a habit of waiting for you to do X-number of jabs on their shield before they do something, like an OoS attack), you can grab them (before completing X-number of jabs, etc.). Alternatively, if they always seem to just wait for you to approach, you can mix it up by just not approaching them; you don't have to play to their game by letting them react to you. Turn it around by making them impatient and have them approach you. If you notice the shield is small, whether it shrank from being held out too long or from your jabs, go for the shield-pierce as you said.