How should I connect my new ceiling fan to the existing wiring?

We bought a new home and are replacing an old ceiling fan with a new one. We had contractors here doing some work that was very bad quality so I fired them. They moved the junction box over (where I’m going to install my new ceiling fan) which I’m hoping was done correctly. I’m only mentioning this because they were the last people to touch the wiring and it’ll more sense as I explain further. I noticed when I took my voltage tester to the ceiling junction box there was no sign of power with the light switch in the "ON" position. Disappointed and remembering that this worked before the j-box was moved I decided to remove the switch plate cover that controls power to the j-box in the ceiling where the old fan used to be. There are three switches there. I recall one of them controlling power to the fan, but I can’t remember which one.

As I started to remove each switch one by one I noticed that two of them had a completely disconnected wire from the switch. What was very disturbing was that wires weren’t capped or taped off with electrical tape. They were completely bare and floating and I could have easily shocked myself or just tripped the switch at the circuit box. This was done by the workers I fired. They more than likely disconnected the power there in order to move the j-box at the ceiling. At any rate, I’m not looking to whine about it, but it’s important info since I’m pretty sure a live hot black wire at the light switch along with the red disconnected wire belong to the wiring I see at the j-box in the ceiling.

There is a red, black and white wire in the J-box at the ceiling. My question has to do with rewiring it so that my ceiling fan will work. I have a Casablanca ceiling fan with light. This is the model that I boght:

https://www.homedepot.com/p/Casablanca-Wisp-52-in-LED-Indoor-Painted-Pewter-Ceiling-Fan-with-Remote-Control-59152/206802477

It’s late so I don’t want to do this now because it’s dark and won’t be able to see what I’m doing. But in the morning I plan to turn the power off at the circuit box. Do I connect the red wire to the switch? This is the switch that has one live hot black wire connected to it. In the junction box in the ceiling there is a black, red, white and ground wire. By the way, the other two switches in the wall junction box at the three gang switch box do not have red wires.

By the way, as I look into the three gang junction box in the wall I see what looks like four white wires bundled together. Two of the switches in the three gang have all black wires and the one I think powers the ceiling has a black and red wire.

And I correct in thinking that one of the switches controlled the fan blades and a second one controlled the light on the fan? If so how can I put my fan on one switch and then hopefully turn my three gang into a two gang light switch?