1) Not quite. Step a doesn't exist. The keeper reveals cards in the room, one at a time, from top to bottom. If one of those cards is an obstacle (perhaps with a puzzle on it), the keeper stops revealing cards there until the obstacle is dealt with -- the investigators don't get to find out what's under the puzzle until they solve it.
2) Correct. Additionally, you don't have to perform a horror check against a monster this turn if you began the turn in the same room as the monster.
3) Each investigator has a turn, then the keeper has a turn.
4) Yes. As long as it's an Attack action of some sort, you don't need to Evade any monsters.
5) Yes. The item is above the obstacle in the stack of cards in the room. When an investigator explores, the keeper reveals cards one at a time from the top of the stack. First, the keeper reveals the dropped item (which was already face-up), and gives it to the investigator. Then the keeper reveals the obstacle, which is encountered as normal. Any items under the obstacle aren't revealed until after the obstacle is dealt with.
6) Checking the relevant portions of the rules:
Page 13, 'Horror Tests' wrote:
Whenever a monster enters (or is placed in) an investigator’s
room (or vice versa), the investigator must immediately make
an attribute test called a horror test.
Page 24, 'Choosing a New Investigator' wrote:
Finally, he places his investigator’s figure on the start space; his
turn then ends.
As written, the investigator will immediately make a horror test. They walk in the front door and are immediately spooked. This fits what you'd expect, since this is the first time that investigator is seeing the monsters.