Then unblock it UNLESS you like gurgling sounds
Your vent pipe for that part of the plumbing is either blocked or non-existent. Having to tip the toilet off center slightly is letting air enter into the system, something that should be happening under normal conditions if the vent pipe were working properly. That vent pipe needs to be snaked out and cleaned.
You PROBABLY have either a partially blocked drain line or possibly a missing or blocked drain vent. It's all behind the walls and if the drain vent is missing it is a direct reflection on the skill and/or integrity of the plumber. If the drain or vent is blocked, that is just a function of home use. A GOOD, plumber can help you figure out what is wrong. Sometimes the solution can be as simple as a stackless vent, but those devices are not allowed in some communities so check with local building code.
Yes if the vent pipe is 4" and vertical by code and there is nothing connected between your toilet tee and where you would connect your new toilet tee. If not worried about codes then yes you can connect to a 3" vent line if no other vent lines are connected down stream. If you have a vent pipe that is less then 3" and or you have other vents connected between your old toilet tee and your new toilet tee then NO you can not connect a new tee for your toilet.
Yes as ALL fixtures need to have the vent placed above the FLOOD LEVEL RIM
It probably has no vent. The vent is used to allow air pressure to get around the material that is going down the drain and prevents the water in a p-trap or toilet from being sucked out as the water goes down the drain past it. Sometimes the vent is there but blocked. Sometimes no vent was installed. It can be a serious problem, especially if sewer gas leaks into the home when the toilet makes that noise.
No
Who needs a toilet
Within 24 "
Yes.
A roof vent can be blocked by hoar frost and to illimate this phonimia you need to increase the vent terminal to 4" If a vent terminal is blocked by leaves or other soft debris the water jetting is one of the best ways to clear it
partially clogged drain or vent, improperly installed vent or drain
Within 24 "