Yes as long as the drain has a trap and is vented
You dont. A tub drain is too small for a toilet drain. You need to hire a professional to find a main line 3" or bigger to tie into for a toilet drain.
The clog is below the point where the toilet and the tub join the drain.
You have to use toilet more
The tub and toilet connect to the same drain at some point. The main drain was plugged but the connection between the toilet and tub was still open. Water seeks it's own level. When the water came up in the toilet, the tub was lower so some of it went there.
The drain is plugged between the tub and the sewer or septic or in the case of the septic system, the tank may be full. The toilet had to go somewhere and the tub was available.
A frost proof toilet the trap is located below the frost line
The toilet itself is plugged or the pipe from the toilet to the drain is plugged. It may be that the tub and sink have their own drain pipe that may connect to the main away from the toilet drain. Plunge the toilet or sometimes if you fill a 5 gallon bucket with water and pour it into the toilet as fast as it will take it, that will flush out the line. It is a greater amount of water all at once an forces out what the clog is.
The drain from the toilet to the main or the main itself is partially clogged or collapsed. There is probably enough room for the sink to drain but the washer puts out so much water all at once it can't get through and backs up into the tub and toilet.
You can use the existing floor drain lines most likely you will have to cut the drain line or add to it to line up with the hole in the shower. tubs have drains on one end while most showers have it in the middle. You can buy a 30" by five foot base from Mustee. Nice product, comes in left or right hand drain.
If you reduce the soil connection to 2" and install a trap
Supply lines- Hot and cold water for each sink, bathtub, Jacuzzi tub, and shower. Cold water for each toilet. Drain lines- one for each sink, bathtub, Jacuzzi tub, shower, and toilet.
15 inches from outside edge of tub to center of toilet flange.
The toilet will gurgle as it sucks air through out the toilet trap. You may even hear it suck air through a nearby sink or the tub. Sometimes it may just drain slow or weak.