What are the fishing regulations about swim areas? How close can I get? Can I cast in them? Are they even allowed to rope off their own areas?
Assuming we are talking a public lake, most things are 100 feet like no wake regulations. You are not supposed to cast in to them either. I don't know if that is a specific law, or will just get someone very angry at you but I do expect the answer would be something along the lines - 'duh, you can't fish inside a legally marked swimming area.'
'Under power' on an electric motor...?? Not sure exactly how that meets whatever law or regulations are out there? Probably one of those 'ask 5 law officers' get 4 different answers kind of thing. I would look it up but I'm swamped right now and it would probably be scattered among 3 or 4 or more different places and regulations.
You're not supposed to put out private buoys for things like swim areas or ski runs without permits. Sometimes the MDNR comes along and makes them remove, reduce or change them. Other times they have been there forever and they stay there. Sometimes they are new and they still stay there. Probably who you know, or who complains either way. Something like that.
The 'ski club' on the Grand River in Lansing had buoys and a ski jump for years. They would even come down and chain off the public ramp whenever they had a 'ski competition.' Went on for years. I tried to launch one day and found the ramp chained off with a hand-written sign from some guy...
Called Lansing Park Police and they said no, can't do that. I think it took a total of 2 years with multiple calls before it finally stopped happening. It took a few more years before they finally removed the ski ramp, then reduced and moved the ski buoys before finally having to remove them completely. They may have been able to leave some longer if they had been more willing to cooperate most likely. I believe it was because they took so long to act, and wouldn't do exactly what they were told that they were eventually told they had to completely remove them.
People want to do what they want to do.
When I'm fishing along and someone with their private swim area starts a fuss I usually just keep fishing along. Maybe speed up a little to get out of the way a little quicker. There are some things I will debate, and some I don't bother. I guess if 'swim areas' started popping up all over the place that might change... I've also had enough times over the years where a law officer of some type showed up and just said to us, 'you have plenty of places to fish, why not just move along to make this go away.' Always enjoy when our rights are stuck up for...

On a rare occasion a law officer actually will tell the complainer they are wrong, or even breaking the law. It's nice when it happens. With the angler and hunter harassment laws it can happen a little more often now but still depends on the circumstances, the lake and who shows up sometimes.