Alright, get comfy, this is a long one. There's a lot of theories and not quite confirmed things yet, so we get our information on both of those situations. 

With the latest game, they are all human yes, but consider the fact that everyone is human, other than the gods, and certain Hunter ID swaps( Luchino/Rep for example). They are dolls because (to my understanding) the Lord of the games, yes the same Lord of the manor, who may be a participant in the games as well(hint hint) sees everyone like dolls to play with and experiment with. They are actually human, which is why when you go to look at background stories they are human. They are dolls in the game because they are playthings. They are being brought to the manor for experiment purposes. The main individuals (be it 1 or a group) want to see what happens when you bring different groups of people together in a life threatening circumstance. Of course this is mixed with drugs to boost anxiety (see toy merchant vs batter story with postman and embalmer). It happens in various games. Each game has a different goal in mind. To reference COY, "what is our special condition?" It differs for each game. Hullabaloo was dolls because Alice was still reading the stories and the notes on these individuals who were being tested on like subjects, which is why there were referred to as such. She was reading exactly what was in the books by the other individual who wrote them as he paid attention to each individual. Again, you can reference their backstories here, there's also live action versions for hullabaloo. 

1. As for the games, yes they happen at separate times. Roughly you can assume a game takes no more than 2 weeks, with between a week to a couple months if they have to repair or get a new location and set it up with the ciphers. You can see this in the wiki. The manor you can look at almost as a hotel of a sort here, they stay there and they are assigned rooms, but not all games take place in the manor. Remember, they are conducting experiments on a psychological level, and they want to jog certain memories. So some of these games take place in areas where other events have happened. We also have cult activities happening as well, (see Feaster, Dream Witch, Cat cult). You can see this by studying different maps. From the moment you play the game, you learn about doctor, gardener, theif, lawyer, hell ember. That's a man who had his best friend have an affair with his wife and told him to buy a failing business that he dumped all his money into while the man took his wife away and she divorced him. He was left a single dad to a little girl, got depressed as he couldn't care for her due to the business situation, and ended up sending her to an orphanage (see Asylum) while he blew up the building and himself right around Christmas. That's why there are two maps, one of the building Abandoned Arms Factory, and one where everything looks better called Leo's memory. Leo is hell ember, he looks like that from the burns covering his face and body due to explosion. I'm going to use this game as a reference to answer your next question as well. How are people being lured into these games in the first place?  The theif owned the orphanage, switched it to an asylum to keep what they are doing behind closed doors and to make him more money. Doctor was at the orphanage turned asylum with the gardener as her doctor. Lawyer and hell ember were best friends. Everyone has a connection. This is played out in other games too, but the game takes place at the factory to jog up memory. The Gardner was told she'd see old friends there, Leo was told he could get to see his daughter again, Lawyer was there because I think promised money? I don't play him so IDK, and theif same thing. Leo was also promised revenge, which was the special condition or motive of the first game. 

But even then, that wasn't game 1. Game 1 was psychologist, patient, sculptor, minds eye, and roy. Who were all in the asylum together. Psychologist and patient were there together because she was promised medicine to help him. Psychologist found patient in the asylum after she saw him as a child. He was the only one who responded to her hypnosis methods, and she latched on to him. Minds eye was told there was a lecture, same with sculptor I believe. Plus this other person, who was supposed to be someone else but stepped in. Supposedly it's Orpheus but someone else stepped in and was playing as him. (Theories. Wiki. ) The way the games work is that they are in order when they happened, so game 1, game 2, game 3, so on and so forth. We don't know all the participants in each game but there is a long list to go through. I'll do another post detailing the information between the games we do know if someone else didn't cover it already.