Cops creating fake profiles to stalk individuals of interest - they violate terms of service of the website...

Civilly, breach of terms of service/use is a flavor of breach of contract and would be up to the website owner to sue the breacher. A website will only sue a breacher if there is some perceived upside to doing so. By and large, I suspect that website owners have little problem with law enforcement using fake personas to build cases around various criminals who may using the websites - so civilly this is mostly a non-issue. And if a given website owner did want to sue some breaching law enforcement, there might be sovereign immunity hurdles to deal with. Now on the criminal procedure side of things, i.e., the 4th Amendment, I suspect by and large that use of such fake personas is not an unlawful search - which likely comes down to a reasonable expectation of privacy analysis. Perhaps there is some recent caselaw on that point or some law review articles - I'm not sure. Law enforcement has a long history of using undercover operations to build cases that is very well accepted. However, I'm sure some officer conduct will stray into entrapment from time to time, but that is a separate legal doctrine from 4th Amendment search jurisprudence.

IF a person uses social media on the internet, they have chosen to lose their ecpectation of privacy. If one is doing something unlawful on the internet, they r likely to get caught.

Police and other individuals routinely set up fake profiles in order to gain access to various websites and social media services. Police especially do it to conduct investigations. Generally webmasters do not bother to respond unless there is a serious violation of their TOS. There is no expectation of privacy on the internet and information obtained as a result is usually perfectly legal and proper. It is very unlikely that any police department would promulgate a rule prohibiting fake profiles.

First, note that I have not researched this question and that this answer represents an initial, off-the-cuff impression. My thought is that although there may be a terms-of-service violation (note I said there may be) I no constitutional violation or other illegality that would warrant suppression of any evidence so acquired. So even if you were technically correct I doubt that your observation would have any practical value in the defense of a prosecution developed through an internet investigation. You would have a tough time persuading any court to adopt a rule that would make the internet a safer place for the activity that is usually the target of this kind of investigation.