A toilet has to be vented otherwise you are trying to force liquid against the air in the drain and it is pulling against a vacuum. It will never flush right.
You need at least a 3 in. pipe -- shower is 2 in. pipe
You can install the vanity first. Then, install the tile up to the vanity and around the pipe for the toilet. Then, install the toilet. That way, you do not have to replace the tile should you ever have to replace the toilet.
put it on ya stink pipe
On a standard toilet in America the drain is 12 inches from the back wall to the center of the drain.
By strict calculations OR install the pipe longer then needed and after the finish work cut the pipe to the required height and install the flange
The highest 4 inch pipe should have a vent on it, or directly above a toilet junction Above the flood level rim of the fixture it is servicing IT does not mean the toilet
you need a hammer arrester. They sell a nifty hammer arrester that will fit on the pipe supplying the toilet without having to use a torch. fairly cheap ($12) and easy to install. A loose washer in the toilet shut off valve can cause this problem.
The main toilet pipe is partly plugged after where the upper pipe joins the lower one.
Install a ty fitting on the stack in the basement then run it to the sink. Put it low enough to account for a fall in the pipe, to allow proper drainage. Be sure to install a waste and vent pipe to code for both fixtures.
Clean the inside of the pipe and floor top with a wire brush. Apply silicon to inside of pipe and top of floor, you are making an airtight seal. Install lead dutchman into pipe and repair flange on top, which will secure the lead dutchman. You can now install your toilet as usual, since you have a flange for mounting your bowl ( this is assuming you are updating to a flange mount bowl).
I would need to know how the pipe you want to use is set. I will guess that it might be horizontal? There is a saddle clamp available that could possible be used. A section of pipe could be cut out and an inlet added. Rubber couplers would be used to connect the two. You also have to consider how and where a toilet would be vented. Is there a vent behind where you are planing to install the toilet and if not can one be added?
It's not the toilet, there's a blockage in the pipes some where after the drain pipe from the toilet joins up with the drain pipe from the tub.You're going to need to have the pipe snaked.