In regards to no.1 - there is no mention whatsoever that the time turner provides you with anything other than placing you back in time, also the map picks up harry under his invisibility cloak (a deathly hallow - quite powerful)
why wouldn't the map show the interior? The whole castle is an interior and the whole grounds are mapped. - i forgot the wording but i do faintly recall lupin saying he saw pettigrew 'leaving with them' but not inside? so I might be wrong.
There is no information that any of the teachers other than Dumbledore and Mcgonagall knew about the time turner (also at the end Snape does come across as sincerely clueless)
This is what I always thought happened without even considering other scenarios before now. Lupin says that he thought the map was getting old / fucking up when he saw pettigrew on it in hagrid's hut - at this point he might have seen 2 harry/herm at the same time and he thought it was just a fault with the map. Also once Sirius appears i'm pretty sure his attention is diverted away from other parts of the map until he rushes off. Same with snape not seeing them as his attention was on the whomping willow. Another possibility is that he was following the trio and the time turned harry/herm were out of range/zoom/focus call it what you want. You can also argue that the map only reached the treeline, and none of the forest - so lupin would never have seen them and once they left, his attention was diverted by pettigrew.
With regards chamber of secrets / room of requirement - these rooms where never found by sirius and co, so i don't think they could have mapped them (I assume making it was like mapping what you know eg. the secret entrances, and not an automatic process of magic which reveals the whole castle)