It depends. My daughter's college had Sororities and Fraternities but none of them had houses. They live in the same section of a dorm. Some Universities control all the housing, and the Fraternities and Sororities have their own houses, and only members live in them, but they are owned by the University. Some Universities have a combination of University owned and privately owned houses. And some Universities only have have only off campus houses owned by the Fraternity or Sorority with no University ownership involved. Every house I am familiar with had a "House Mother", usually an older single woman. Never have seen myself a "House Father"
As for Pledging, again, it depends on the University. I think almost all have "Rush", a time period when the Fraternities and Sororities have open houses to show off what they offer and stand for, and potential members show off what they can offer to a house. Some Universities allow Freshman to join and move into Fraternities and Sororities. My University allowed you to Rush after you had completed your first semester Freshman year, but you could not move in until your First semester Sophomore year.
As for accomodations, again, it depends. My Fraternity owned 2 houses next door to each other, and a third house 4 doors down that we leased (from the University) off campus, right across the street from Campus. Our main house was a 6 bedroom, 3 bathroom 4,500 square foot house that had an apartment for the house mother, a commercial kitchen (we employed our own cook), and a dining area. Individual rooms generally housed 2, there was one 3 person room, and one 4 person room. This house was built in 1939 as an off campus girls residence, so it was built as basically a small dorm. The house next door was a regular 3 bedroom 2 bath residence, with the Dining room walled in to add a 4th bedroom. It had 3 two person rooms, and 1 one person room. The third house, the leased one, also was a residence, 3 bedroom, 2 bath.
However, some Fraternities and Sororities have sleeping porches. One big room where everyone sleeps, but small individual rooms to store your clothing. Now, I have been in Sororities where there is one bed in the individual rooms, but those are only supposed to be used when someone is no feeling well.
As for room and board cost, it can vary. University owned Fraternity and Sorority houses often charge the same rate as living in the dorm plus what ever social and membership fees the Fraternity and Sorority charge on top of that. Privately owned houses can do basically whatever they want. In my case, the total cost of everything, room board and all social fees was less than the dorm. Some Fraternities and Sororities do not offer board, and either have a kitchen where you can prepare your own food, or you have to buy a meal plan from the University dining hall.
Long answer, but sounds like you need to be asking a lot of questions about the Fraternities and Sororities at the specific University you are interested in.