Water supply to toilet is off

In almost all cases there should be a shutoff valve behind the toilet, just follow the visible pipe that comes out the bottom of the toilet tank. It will either be a globe valve that has a handle you need to turn many times to open/close, or a ball valve with a handle that you turn 1/4 turn to turn on/off.

If there is no shutoff valve, you would need to turn off the supply to your entire house. It would also be a good time to install a dedicated shutoff for the toilet.

All these lines are connected, but it's not easy to say how without inspecting under the floor. I'd say there's a good chance the shower, possibly sink too, are connected to a one vent, and that drain is a wet vent for the toilet where they join further down stream. Then everything runs down to a main stack. That would be a fairly typical setup.

If you see bubbling in the toilet from the bath, or hear gurgling in the tub from the toilet, you may have a problem with a blocked vent. Otherwise, some movement can be expected. As the water rushes past the wye connection to the toilet, it causes some pressure changes pushing the water up or pulling it down on the other side of the trap (the toilet bowl). You're also likely to see that on a windy day just from wind blowing over the vent pipe on the roof. Other traps do the same thing, but you can't as easily see them.