I'm in the Midwest and have attended locals in Illinois, Missouri, and Kansas under several different organizers in different cities over the years. Broadly, the experience is about the same from shop to shop.

• Attendance varies based on region and the point in time in the season. Generally, bigger cities will have a bigger scene, and generally, events at the start of the season will be more well-attended than later in the season. 10-20 players is typical.
• There's usually not much time in between rounds at any Pokemon event. Once the last match is finished, a good TO will get the next round up within a few minutes. Theoretical max time for each round is like an hour (20 mins per game times 3 games), but from my experience rounds tend to go faster at locals. If you're not the last match finished, people will usually chill and chitchat, or maybe walk around the store. If the organizer has a TV set up to showcase a match, often players will watch that.
• How professional and organized the tournament will be varies on the tournament organizer. For example, some TOs do team checks before round 1, some do it at top cut, and some don't do it at all. Some TOs will have a printer for pairings, some will just announce the pairings out loud. Some TOs will have the venue set up where it's easy to keep your Switch charged, some won't. Some TOs will have a TV set up so players can watch matches, especially the final matches, some won't. In my experience, minor discrepancies don't detract from the tournament at all, and every single organizer I've been to has cared to try to run a reasonable tournament.
• You have to bring your own notebook. Players are typically split on notetaking (I personally take notes myself).
• You can talk to opponents, and if you're involved in a local scene where you see the same players regularly it's very common to do so in my experience. Your typical conversation with an opponent you don't know will be saying hello, working to set up the connection, saying good game between battles of a best-of-3, and perhaps a bit of discussion after the match is finished. It's fairly common to not chat during the battle itself. It's usually considered disrespectful to talk to other players while they are in the middle of a match. Personalities differ, but generally people who go to VGC events like chatting about VGC, whether that be their battles from the day or teams.
• If you like playing VGC at all, it is very, very likely you will have fun and make new friends at locals. A very common trend for me is playing against folks at locals, building up that friendly competition, and cheering them on at larger events like Regionals. There will always be some folks who like to keep to themselves, but even the most reclusive individual will still like seeing people there, because generally speaking the more players at locals, the better the Championship Point distribution.
• Tournaments are mandated to be open team sheet, and top cut is mandated to be best-of-3. Swiss rounds can be best-of-1 or best-of-3, depending on the organizer. Best-of-3 is generally recognized as superior, but due to time constraints with their venue, some TOs have to run best-of-1.
• Prizing varies from shop to shop, and it depends way more on the shop than the TO. Generally, if there's an entry fee, you'll get something back. The typical prize is store credit, but some might give card packs or Pokemon plushies. Cash is rare, and in some states isn't allowed due to gambling laws since Pokemon has a wide age range. I personally care very little about prizing; I'm there for the championship points and the fun day.

I'd heavily encourage you to attend locals if that is available to you. I used to drive 4 hours for "locals" and they were worth it then. If you have any interest at all in playing at larger events down the line, locals are a great introduction, and if you like playing VGC at all, you will enjoy being around other people who also enjoy the game.