This is just modern football. A bunch of football people furthering their own interests and/or those of the people they work for.
-In terms of whether this happened, I suspect it did, in some form, as the denials from United and Raiola don't actually deny it happening. Whether or note we would have sold to City, in Jan or otherwise, or whether Raiola would have contacted Pep directly, really isn't the point. Likewise, Pogba's post on Twitter doesn't look to be designed to do much more than get people talking.
-Offering those players suits Raiola's agenda. He doesn't give a shit about United. We're just a big, dumb organisation willing to line his pockets. If someone would pay more he'd link up with them without a second thought.
-I doubt Raiola would have done this without Pogba's knowledge. But equally it might be that Raiola does this stuff on his behalf, to bring about a particular result and Pogba doesn't concern himself with how the sausage is made. Raiola and his ilk are paid to be the bad guys in the eyes of the club.
-With regard to why he'd have made the offer, it could have been for a few reasons:
First, that he actually wanted a move. I think this is unlikely, but not out of the question, as he's already left us in difficult circumstances once and will, I suspect, do it again given the time, albeit I doubt he thought that we'd sell to City. Without even mentioning that he seems to having issues with Mourinho.
Second, it may be to get him Pogba a better deal, particularly in light of the Sanchez deal. I imagine this is most likely. Raiola's no fool. He knows that something like this can be used to exert pressure.
Third, Raiola may have known that offering him to City might bring issues with Mourinho to a head, or make other clubs aware that he was open to a move.
Finally, given the closeness in terms of timing with Mkhitaryan's move, it may just have been him rattling a few cages and playing whatever cards he had at his disposal.
-With regard to Pep, I have no idea why people think he shouldn't throw this stuff back in Raiola's face and, in the process, use it against us at a time when City are being criticised and with a game against us coming up. The use of the word dog was obviously a reference to Raiola's original criticism. Guardiola certainly doesn't owe us anything. Our own manager consistently unsettles teams when given the chance. It's just part of the usual bullshit bingo.
The tl;dr version is that almost everyone involved is an insufferable twat and, if you're daft enough to have expectations of them or put your faith in them, you'll probably be let down.