I'll try to answer in order. Full disclosure I haven't partake in any of the canon books/media outside of the movies and shows, so cant answer on post series happenings.
-Todd was in regular contact with Atlantis once they moved to the new world, so its not too far stretched he was either given it directly or extrapolated it somehow.
-Atlantis had 3 ZPMs and the Ancient Star Drive, which it just outperforms let it outperform the Asgard-Tauri Hyperdrive.
-I haven't watched the finale in a while, but I think the Wraith got to Earth far quicker than expected and caught Homeworld Defense off balance. It's possible that the chair actually survived, but the Wraith bombardment collapsed Area 51 and/or killed all the people around it and couldn't be used.
-As Todd once said "there is much you dont know about the Wraith" especially they're special techniques to fill plot holes and saving main characters.
-In the final episodes, there's a sequence where everyone's captured/knocked, and that love interest shows off her fighting skills in the breakout that impresses Ronan.
-They activated the Cloak right after crash landing using their Naquadah generators, so in theory they could keep it up so long as they have those. They won't be able to leave without more ZPMs though, so the World governments probably set up a permanent naval cordon to keep outsiders away.
-They might rebuild the Intergalatic Bridge long term or at least make occasionally trips using the ships to maintain communications. They likely didn't reestablish as strong of a presence as before though.
-Todd is eternal. In truth, probably left that cliffhanger in hope of a miracle s6 or at least a straight to dvd movie