Re: whether Mance knows Jon went back to being a crow, I was reading some recap type of article somewhere and it said that once he pulled the switch-back, the crew he was with (red-beard and co.) sent a raven message to Mance to inform him, and upon getting that message, his response was to send the cannibal dudes up to join that party. The author mentioned that as part of a rant about how dumb the wildling crew has been, calling that sequence to be an insufficient or otherwise objectionable response to the news.
I personally don't remember that all being shown, but I also cant recall any other explanation for the cannibal arrival - they just showed up at some point and there was some killing of some randoms involved. So it makes sense thats how it went down and that Mance knows full well Jon = enemy.
Even if thats wrong, its been a long time and would be hard to imagine that the group who knows he switched has never bothered to inform Mance in some way. Plus the wildlings have the wargs that have been spying on the wall personnel and they'd have seen him.
It would be a pretty big stretch if they are really moving ahead with Mance being unaware and using that as Jon's method of killing Mance.
But that brings me to something that's incomprehensible - why in 7 hells did Jon give Sam his sword before heading out on his solo mission? It's basically a suicide mission with him fully armed, but rolling into enemy-infested territory with no clue where Mance even is, limited to about 24 hrs before assault 2, without even bringing any type of weapon? That's a level of nonsensical that I'm not sure I've ever seen topped. I hope he comes across some 70 year old consumptive wildling, who does have a sword, chilling by himself, and then promptly getting killed by him in the short-lived bare-knuckle vs sword fight. End of Jon Snow.
And as a final note, even if Jon said the attack was merely a kicking the tires mission, I don't buy it. Nothing else about it gave any indication that was the case. I remain fully convinced that the battle just stalled and the remaining forces indeed decided "they'd had enough for one night", as the NW dude said as they retreated.
There were 4 main components of the battle
1) attack from south (2) attack from north (3) force access to the tunnel (4) attack by climbing wall. 1 and 3 and 4 failed and 2 wasnt really going anywhere, so they fell back to take another run. Not by design. LAI