No.
The difference between a gully trap drain and a floor drain is placement. A floor drain is in a floor, a gully trap drain goes on an external wall.
Floor is sloped toward floor drain for draining. Floor cleanout is level with floor and is used to clean out drain line.
All you will need to cut out is the hole for the drain, probably 5 inch circle. The ceiling below and how you route the drain is always different.
A floor drain , drains water and other liquids that spilled on the floor
The drain from the washer to the main line is getting plugged and the floor drain is easier. Drain cleaner in the floor drain should take care of it.
By finding and repairing the leak.
Because the second floors ac unit`s drain line is either terminated above your utility room or the primary drain is now plugged and the unit is overflowing into the space(above your utility room).
Same way as the first floor. The drain has nothing to do with the way it is installed, your just not adding a drain. Which is a real bad idea and should not be done.
Not much other than the floor slopes into a flor drain so any water or other fluid goes directly into it while a floor sink is bigger, sometimes has a strainer in it but pipes can be ended directly above floor sinks so that the fluid from the pipe flows pirectly into it
You would have to build a platform for the tub to sit on. About 3 inches if you are using a floor drain. There is a trap right after the floor drain so you would not need one at the tub. If possible you could position the tub directly over the floor drain but that would eliminate the floor drain which would be a problem if the basement every flooded.
The toilet flange is usually above the floor level. You would have to cut it off the drain pipe and cap it. How you do this depends on what type of pipe the drain is made of. Even if the drain should be below the floor level, you have to seal the drain or sewer gas will come up from the drain.
depends on the size of drain piping. Most toilet either have a 3" or 4" drain. The size hole needed would be larger than the outside diameter of the piping. 3" pipe=4" hole / 4" pipe=5" hole