You need a basement toilet system. There are 2 basic types, one has a small pump that pumps each flush or use of a faucet to level immediately. The better system has a 40 gallon bin fitted in the basement floor with a septic pump in it. This operates on a float switch and pumps about 25-30 gallons of liquid when the switch is triggered.
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.
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 clog is below the point where the toilet and the tub join the drain.
Probably leaky drain pipe form toilet which passes through that room. Work out which corner of that room is below the toilet, you will probably see a swelling in the wall where the drain pipe is hidden. Call a plumber and get him to fix it.
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 toilet wax ring is probably cracked and leaking.You have to drain and remove the toilet to replace the wax ring below it.Hope this helps!
Usually toilet flange is glued down onto plastic drain pipe. There is a toilet flange that can be glued inside of plastic drain pipe also.
Yes as long as the drain has a trap and is vented
The toilet is 3 or 4 inch and the shower is 1 1/2 or 2 inch. You could reduce the toilet to 2 inch, but it would never flush correctly or be of much use. The current toilet drain has no trap in that section because one isn't needed. The toilet itself is the trap. If you are using existing waste lines, they should already be connected to the vent stack. If you are adding lines, connecting to the existing stack is fine as long as it is above the last drain.
On a standard toilet in America the drain is 12 inches from the back wall to the center of the drain.
The drains for the shower, toilet and sink all connect to a common line. Assuming the toilet is not backing up, the problem indicates that there may be a partial blockage, enough so that some of the toilet flow is backing up through the shower drain line. You need plumbing repair. The shower leak you mention should only be in the shower, or else you have a broken drain line as well.