1. I just started playing yesterday, with The Fall of House Lynch. My friends John, Jenny, and Sam were playing as the investigators (in that order), and I was the keeper.

After we flipped Clue #2, John was in the hall with the zombie. Jenny then took her turn, damaging the zombie and lighting the room on fire. She left the hall with her remaining move and did not receive damage. What we could not figure out was whether or not John received damage because he was already in the room and his turn was over. I decided that his turn in this round was over, and as he was still in the room after his turn, he received damage. Jenny and Sam agreed with me, but understandably, John was not happy.

Later in the game, John moved my maniac into the room on fire. Jenny, Sam, and I agreed that the maniac did not receive damage, as my turn had yet to come in that round, but John insisted that the maniac should receive damage. (It ultimately did not affect the maniac because I fully restored his health and moved him from the room during my turn, so I accepted the damage to appease him.) My understanding is that each round has a definite end because time has passed, so an investigator staying in a room on fire for a full round would not just be waiting until he could move but would be stuck there (in game time) for hours.

What is considered the end of an owner's turn? Is it the end of his turn in that round (meaning if his turn was earlier in the round, he receives damage) or the end of his next turn whether it is in this round or the next?

2. John's character did eventually die, and he came back as another investigator. During this time, my turn as keeper came up. How many threat tokens should I have received? One for each player or one for each currently-living investigator?

Then, at the end of the game, Sam escaped the mansion, and it was my turn to collect tokens again. John and Jenny were still alive and in the mansion. How many should I have received?

I am not sure what causes the confusion here. "The end of the owner's turn" is rather specific if you ask me. If John has completed all of his actions, his turn has ended. If he is then standing in a room which is on fire, he gets damaged. But if the fire gets there at the start of Jenny's turn, then John does not get damaged unless he is still in that room at the end of his (next) turn. However, when Jenny ends her turn in that same room, she does gets damaged.

Same with the Maniac. The "owner" of the maniac is the keeper, so if the maniac is in that room at the end of the keeper's turn, he also receives damage.

This rule allowes every player to move his/her character (or monsters) out of the way.

As keeper, you always get the amount of threat as the amount of investigators you started the game with. People dieing or escaping the mansion do not change this unless specifically stated in the special rules of each scenario or on a card.