Well, firstly, to let them know that they were beep (i.e. the crew would know that, since Donnie was a rat, he would have provided the FBI with a wealth of evidence including recordings, surveillance, phone taps, etc, to back him up).
Secondly, to give them a chance to confess, rather than go to court. Or to give any underlings a chance to rat on their superiors (maybe get some kind of pardon?)
Thirdly, because if the case/s went to court then Donnie's background would become public knowledge. Or maybe it would come to light sooner or later anyway

Of course they believed it, they just weren't gonna give the FBI the satisfaction, or incriminate themselves.
As for them being there. it was to show that he was an FBI agent and not a rat and if harm came to them it would lead to trouble from the entire justice department. It also is to scare them into thinking about cooperating with the investigation, and so that Sonny woukd go back in the club and make calls to other mobsters higher up. The phone was tapped and it's a RICO case, if Sonny gets the higher ups to acknowledge the situation on a tapped phone, they have them on the hook too.
I think you're the opposite of paranoid, I think you walk around with the delusion people like you.

I was watching a doco about the New York mafia where they interviewed the real Joseph Pistone. As part of the show, he took them to a few of the scenes where actual events in the movie occurred. During one such segment, someone drove by in a car and yelled out "fking rat".
Long memories I guess, but it made me wonder if it was genuine or staged?

i have nothing but respect for Pistone
he was swimming in sewage for years and he never drowned

My pleasure.
The movie (for whatever reason) portrays the FBI as heartless users of Pistone, not caring what happens to him. He himself sets the record straight in the book (the edition after the movie).
I mean think of it, would it make sense otherwise to tell them about Pistone before they're even arrested? That would only make them freak out (an undercover unlike a simple rat carries much more weight in court) and would be more likely to take desperate measures to tie loose ends, something the Feds wouldn't want (not if they want to get to the top guys).
The best moment to show off evidence and so is when the bad guys are in jail, safely monitored and unable to have others killed (usually) and with nothing to do but go steer crazy and race to cut the better deal

Seems like the definitive explanation. I hadn't read the book, so thanks.

The book makes it pretty clear that was the reason:

• Unless proven without a doubt he was undercover, the mobsters would assume he turned rat and thus put contracts on him and his whole family.
• But proving that he was undercover, the FBI was saying "back the HELL off from him. He's law enforcement, not a rat, thus he was simply doing his job, and he beat you fair and square".
  The FBI got wind of contracts being put on Pistone and his family indeed, no matter who he actually was. And thus paid visits to every capo and boss they could locate (of all the crime families) telling them that if ANYTHING happened to Pistone or his family, they personally would become the entire Justice Department's (not just the FBI) b!tch.
  They made that specific threat to Paul Castellano (head of the Gambino family, the most powerful one).

"I mean they are obviously not bright individuals" that coming from a guy asking this exact question is quite amusing.

THAT'S RIGHT! I AM LAW ENFORCEMENT AND THAT IS THE OPPORTUNITY TO LET THEM KNOW "COME ON IN AND WE WILL PROTECT YOU IF YOU CO-OPERATE"

The FBI knew the rules of the mafia, and they knew that for letting an agent get in so close with them, Sonny and Lefty were going to get whacked.
This was their way of discreetly saying that there was an alternative, come in and talk and we'll protect you. But they were too dedicated to the life as you see in the movie. In reality, Sonny went to his death knowing he'd be killed and Lefty was arrested on the way to his.
Well she turned me in to a newt! I got better!

lovely touch when donnie argued w wife, but still opened her car door.

Another thing reason besides those already given is that in previous scene Donnie tells his wife that he does not want to pull out, because when he does, Lefty will be killed.
His mission was already terminated, but they wanted him out, by telling them about Donnie he effectively don't have any reason to go back, Lefty will be dead, and he will be too if he stays.

The agent tossing his business card dismissively on the table and saying to call him if they want to talk made it pretty clear he was there to both gloat and offer a chance to turn state's evidence to save their own lives.

The book claims that the agents that went to talk to the crew, were agents the crew already knew. There are certain agents in the FBI assigned to certain crews, the hunter and the prey. So they knew if it was the agents assigned to Sonny's crew, telling them Donnie was a FBI agent, it would carry more weight.

True.
But the cat would be out of the bag for Pistone's cover once he showed up to give evidence during their trials in his FBI suit talking like a college boy again! HAHA

Exactly right Koji. There was also the part about them telling the mob Pistone was an agent not an informant and it would be a really bad thing for the mob to go after an agent or his family. Nobody really cares that much comparatively about an informant.

Simple. The movie is a bit different than real life, but it was close to accurate.
Sonny Black was a capo who would have to scramble and make important phone calls to inform the higher up's of his screw up. Important conversations that would implicate them. They had a court authorized tap on his phone. Keep in mind at this time, The mafia was still a superpower and they had yet to beat them in court and convict higher up the chain. RICO gave them the power to convict bosses even if they did not participate in the crime. Merely if they ordered it.
In the movie, lefty is the guy Donnie is closest with, but in reality, it was Sonny Black who Joe Pistone truly got close to as a person. And Sonny Black who gave the bartender his watch and jewelery before going to his final meeting. Lefty actually was protected from being killed by the FBI because they got to him in time and died of cancer years later.

Putting pressure on them was a technique to get them to talk. To shock the WHOLE GROUP of them in one moment with all those photos of "Donnie" was a really good shock value act. Try to shake 'em up into talking.
Unusual tactic, but your explanation does make sense, though I have no knowledge how the FBI operates, of course.

Exactly. I was starting to think I was the only one to know this. I think they make it obvious that Sonny Black is just saying it's a trick so that Left would stay calm and not freak and pack up in the middle of the night and run away.

Bingo - agreed 100%. Why would the FBI doctor photos and go to all that trouble. Sonny knew and was just saying that to keep all calm and plan things without getting Lefty antsy.

In the film I believe Sonny Black was genuinely unsure immediately after the bad news. I doubt he was putting on an act for Lefty. I only say that because Sonny Black knew his head was also on the chopping block if Donnie was FBI. Sonny was more worried about himself.
He killed sixteen Czechoslovakians. Guy was an interior decorator.

I assumed in that scene outside that Sonny Black and most of them knew damn well that the FBI was telling the truth, but Sonny was lyin about it being a scam to keep Lefty calm and not think he'd be killed soon.

It gave all the guys on the crew fair warning that if they wanted to turn state's evidence against other crews and wise guys, now was the time.
It meant they could go back inside the social club and talk it over and decide if they were all going to give up other guys.
Putting pressure on them was a technique to get them to talk. To shock the WHOLE GROUP of them in one moment with all those photos of "Donnie" was a really good shock value act. Try to shake 'em up into talking.
Waltzing into the sacrosanct social club territory that these wise guys "owned" and used as their protected club space also was a huge f-u from the FBI agents.
They were letting them know who was in charge now. It was a total disrespectful invasion of their sacred territory.

Nothing was given away that was not soon to become public knowledge.
True, but why take the risk of stirring things up? Surely it cannot help the arrest process. I understand this was done in the true Pistone story, according to Wikipedia, but it still doesn't make sense to me why they would do that.