1) "how can lucious and the engineers be working on THE BAT, didn't it get atomized in the nuclear blast?"
- yes, that BAT did. but the armory has several versions of all the vehicles and equipment. more than one tumbler, and other gear. and lucious even tells bruce that they have a BAT that comes in black as well. the one the engineers and lucious are working on in the end is a prototype version, and is not even black. its a blue/grey color. Bruce fixed the autopilot via a software patch, not a mechanical fix. So then you could presume that it became native across all the BATs in the armory.
2) "what happened to the pearl necklace?"
- selena is wearing the necklace at the end of the movie. if you don't focus on the bruce reveal, you can see her on the left, and her profile. however, the sunlight and her white skin make it hard to see the offwhite of the pearls. but it is clearly them, once you focus on just her and not bruce.
3) "how the hell can bruce get back into occupied gotham?"
- when gotham is first taken over, Bane's lead henchmen (small bearded guy) goes to the bridge to tell the National Guard guy that they want to negotiate for a stream of food and supplies. Then later you see the special forces guys sneak into gotham inside of a food truck. So it's very reasonable to presume that bruce was also able to smuggle himself back into gotham. It's a prison gotham. Not a problem getting in, the problem is getting out.
4) "how the hell did bruce know where to find alfred at that cafe?"
- because alfred f**kin' told him where it was! earlier in film, he tells him it is a cafe, in florence, overooking the banks of the arno. after that, I will presume that bruce knows how to do recon and track someone down. especially an old white brit vacationing in florence. not um...not to impractical.
5) "is blake now gonna be robin to bruce's batman?"
- I don't think so. This is nolan's batman story. and like any movie based on a series of comic books, it does not necessarily have to be setup like a comic series. wherein the heroes and villains always fight and SURVIVE, so as to do so again another day. this was nolan applying realsim to the mythos, but not literal realism, because its not practical. he made it more believable than say burton's batman, and definitely more grounded that schumacher's schlock.
so with that in mind, bruce can't always be batman, his body would become dust, he would not be able to handle it. plus, he created batman to be an enduring symbol, long after hes gone. he thought Dent would be able to continue the work, legitimately, but he was wrong. but he realizes he needs to stop at some point, and another must take over. this is alluded to several times in the movie. Alfred wants him to stop, and live his own life, to find peace. Bruce explians to Blake in the car that batman must go on, even after bruce dies. He makes the comment to Blake about why you have to wear the mask. That tidbit about how to throw the grenade (possibly him just showing him "the ropes") or not.
The hard part was really Bruce having to come to terms with letting Batman go, truly let him go, and moving on. Not just going out in a blaze of glory, like Alfred was starting to see. Bruce was no longer fearing death, which means he wasn't appreciating life. that is what "true believers" do. and it is a weakness, a copout. That is Bane and Talia. Bruce has to not lose faith, hope, or spirit. He must fight on, to live. If he then encounters death, he must not be afraid, because he fought to the bitter end. he shouldn't be stuck in this despair as he was after Dent and Rachel died, feeling that he just need some scenario to happen where he could finally die as batman.
6) "so then blake is now batman?"
- it seems so. bruce wayne is dead. but bruce wayne found happiness, moving on. fresh start. possibly romatically with selena, or just friends. who knows. Blake will train, over time. and eventually be batman. gordon has a new signal to call upon him when need be. yada yada. in nolanverse it makes sense. events only have to happen once, not over and over for them to be stuff of legend. so yes, technically in this movie, Batman did fight alongside ROBIN. and like the books, robin does eventually become batman (as well as nightwing) And in other films Batman did enconter his greatest nemesis/challenge, THE JOKER. Harvey Dent did become twoface. but nolan not concerned with a franchise. and the aspects and basic ideas of characters are explored. Ras Al Ghul may not literally be immortal here. but his idea is. his plan is. and that is something that Bruce could not stop just one time. And the villains aren't always killed off, they are caught (joker, scarecrow), die (twoface) or unsure (bane was blasted with a cannon, but maybe he survived, who knows. its up to you)
7) "so bane is just a stupid henchmen?"
- not necessarily. the buildup and perception by everyone was that Bane was acting alone, and that he was this "outside the box" wacko that even Ras al Ghul couldn't stand. and that is what leant to his presence and evil stature. but the reveal in the end, was that he was really just a glorified guard dog for Talia. his only weakness and devotion was his love for her. She was the mastermind behind everything, and since she was in the shadows and all, and he in the foreground, then it seemed like he was the diabolical mastermind, always one step ahead. in the reveal, as she's attaching his gas mask back, you see that he loves her. and cares only for her. since she was a child. he's even crying out of his right eye. combo of recollecting how they meant, as well as getting over the few moments of pain he was enduring as batman ****ed up his mask. Talia's reveal does not lessen Bane, it clarifies who he is. its kinda tragic, in a way. (yes, i cried !!!)
8) "but bane was thrown out for being a loon!"
- no, bane was thrown out of league of shadows because of Ras al Ghuls' guilt over losing his great love/wife. Bane reminded him of the hell she was left to die in, and it hurt too much to see bane. so he threw him out. Talia took pity, and was loyal to the man who had protected her. but bane's thinking was not radical. it was no more different than Ras'. He wanted to destroy gotham by having everything kill each other with that fear toxin. Bane & Talia just wanted to cut out the middle man, and blow it all up.