If they want to act as high schoolers, you'll need to treat them like high schoolers.
I've taught in high school for a little time and while your semester already started, it is not too late to get a handle back on your class. The first few minutes after the class start is the most important moment to make it clear messing around will not be tolerated.
I would try at least once, at the beginning of a class, to say something like this:
You guys are being hard to manage and I'm sure you're aware of it. You are being disrespectful towards me, the rest of the teaching staff and other students who are trying to work. I'd like to know what is wrong, is there anything you think might make your experience better?
This way, you make it clear you want to work with them to find a solution and that it is bothering many people. Give them a chance to work it out with you before going the "full authority" route. You might give some troublemakers to turn into "positive leaders".
Even if this works, you need to start making it clear who has authority in your class. When you start your class, state your rules and don't move away from them. You'll probably need to set an example a couple of times before your students understand. You need to systematically apply the rules you gave your students or else they'll start exploiting you.
Regarding what you said in your post:
People asking literally the same questions over and over
Offer the student to come see you after class if they asked a question that was already asked, this way you do not slow down the pace of your class and if it's an attempt at "trolling" the student simply won't come to see you.
Your school clearly has a policy against plagiarism, start using it without exception. These students lost their right to second chances. If you catch plagiarism, report it to the correct instance at your school and let the comity in place decide.
Students pretty much insulting the lecturer and staff or laughing (sometimes at others asking questions)
Respect is the most important thing in a class. If a kid in high school (where, at this age, education is a right not a service) can get kicked out of a class for being not being respectful, so can an adult. If I paid 10k$ for a class, you can be damn sure I'd stop this after being kicked out once. If you want to make sure you won't have repercussions, go see the head of your department to make sure they have your back if something happens.
Being noisy during lectures
To be fair, this can happen. If this is repeated, refer to the point above.
You said in a comment
"That is a straightforward solution but the lead instructor in this case does not want to take authoritarian measures. So that's another challenge here"
This is sad but University teachers aren't often good at managing this kind of class (because they don't have much experience with them). You should try talking to him/her about it, stating that it really messes up the flow of the class, the confidence of all the teaching staff and the overall credibility of the class.
As a last resort, when your class gets out of control, stop talking. More often than not, the students will deal with themselves and silence should come back to the class. If it doesn't well it is their loss.
To make this work, the best case scenario would be for the whole teaching staff to be on the same line and to make sure your boss has your back, but University students are customers of a service under certain conditions. If some students mess up with your class, they interfere with the students who are respecting the rules and this is not acceptable.
I've seen an OP's comment stating:
"That's basically the case. No one academically that advanced afaik but we have bigwig corporate managers that can barely use computers alongside software engineers wanting to learn about data science and everything in between"
This is a very complex problem to address, because it is hard to pace your class for the large diversity of backgrounds, which means either some students won't understand or some will find the class too slow and since you're alone, it's hard to find a middle ground. What I might propose is to:
- Either match students of different backgrounds together so that they can help each other (by whispering, of course) regarding their different expertise.
- Show examples that can "talk to" your different kind of students. You have, maybe among others, managers and software engineering students, so try to give specific situations/examples where each of these students can bring their expertise. It is likely, I think, that your problematic students are the kind of people that like to hear themselves talk. By getting them to participate, I'm pretty sure you'll be able to have a better handle on your class.
In the case of a professional education class, I think it's important to let the students talk/participate in class. These are not people who are used to sitting hours in a class to listen to someone talk like University students are used to. By giving more opportunities to participate, you'll probably have a better experience.