Treat Super Powers Like Gun Ownership
The US legal system already pretty much addresses this problem in the form of "aggravated" and "reckless endangerment" crimes.
To dissuade the use of deadly weapons, the sentencing for any crime becomes more severe anywhere a weapon is involved in the execution of the crime, even if it is not used to harm anyone. If you rob a store with your bare hands, it is robbery, but if you use a gun to do it, it is aggravated robbery. Using super powers to rob a store creates the same sort of unfair, traumatizing, and increasingly dangerous sort of power dynamic as a gun; so, when a super does use their powers in a crime, the punishment is elevated which would hopefully be enough to convince at least some would be criminal supers to commit crimes using their mundane abilities as much as possible.
On the same token, carrying a gun is not illegal, getting into a fight with a gun on your person is not an aggravated crime, shooting a gun in a safe environment not illegal, and being a super is not illegal. Supers are allowed have powers and use them in ways that common sense would tell you are safe and legal, but using your powers recklessly (like firing a gun blindly into the air) is a crime unto itself. This leaves the subject of using one's powers somewhere along the vein of, if you are not sure it is safe, you can get in trouble for it.
There may also be certain zero tolerance zones, like gun free zones, where using powers is entirely forbidden.
The advantage of treating all powers like gun ownership is that you don't criminalize anyone for having one power or another, you only criminalize its misuse. Using mind control to steal a car is still grand theft auto, but now it is aggravated grand theft auto. Using super strength to crush a person's skull is still murder, but now it's aggravated murder. Creating a situation that blinds drivers is reckless endangerment whether you do it by throwing eggs at their windshields or by conjuring up a smoke screen. The definition of crimes are all about what you are doing instead of what powers you are using to do it; so, you can keep your code of laws relatively fair and simple.
As a bonus, this approach to super power law would be pretty consistent with normal people law such that it would work even outside of their own special culture.
Side note: in some countries, people with unordinary physical abilities like formal martial arts training can be prosecuted for aggravated assault even without a weapon. In a since, these jurisdictions already handle "super powers" this way.
Addressing your specific concerns
Moral implications: Legal systems are about ethics, not morality. The general rule of law is that that which is not illegal is legal until it is not, and any moral implications beyond that is not for the courts to decide. Transferring the mind of a person with a terminal illness into the body of another that is otherwise brain-dead is perfectly legal as long as you can prove you are not killing either person in the process under the current definitions of murder. If it does kill one of the people, then you would need to petition legislatures to define this action as an exception to the law. If it's not illegal, but congress sees it as a "form of murder" then it could be made illegal.
Also, most US states also use precedent in the evaluation of the law to stand in for congressional decisions until the law can be refined. So, the first time someone decides to press charges for something ambiguous like this, it could be decided very quickly if it is considered murder or not by the first court case that evaluates it. Then everyone knows if that strange thing is or is not murder moving forward.
Excessive Damage to Property: Damage to property laws should suffice. The plaintiff brings you to court, damages are assessed, and you are required to pay restitution, and if the damages exceed a certain amount or your ability to repay them, then there can be felony charges that stack which could result in jail time.
Conduct of those with potentially intrusive abilities: Laws concerning fraud and coercion are generally left intentionally vague because people are so creative when it comes to finding new ways to do them. Fraud is defined as any intentional deception or misrepresentation used to benefit yourself or someone else, and coercion covers any use of threats, commands, and any use of force. So, if you can implant false memories or impulses directly into someone's mind, that is clearly Fraud. If you tell a person to jump off a bridge and they do, that is coercion. So, without modifying the law at all, most of the more insidious intrusive abilities are already covered.
As for simple mind reading, there are no laws to prevent it, but there are many laws to prevent the use of said knowledge. You can steal someone's PPI sure, but using it to take their money is theft, using it to get into their digital accounts is hacking, and using it create accounts in their names is identity theft, using it to ruin a person's reputation is defamation, using it to manipulate them is blackmail, so on and so forth.
If you really want to crack down on psychic intrusion, you could expand CFAA law to cover the misuse of psychic abilities according to the same criteria that we evaluate hacking, since psychic intrusion and hacking are so similar in nature.