Call a plumber.
You can just extend the waste line from wherever it is currently to where the new drain point begins, its much easier connecting into an existing line than to try create a new one.
Yes a clogged VENT pipe can cause a sluggish drain
NO, just duct it into the soffit. you can also get the indoor kit that is made for a dryer, but at some point you should install a vent to the outside,there are tons of vents.
By checking the vent to make sure its working and that no one installed an AAV
vent in bathroom manditory
Heck no as the sink is higher then the basement drain and water does NOT flow up hill BUT it does seek its own level BUT you can connect a sink drain to a basement drain if you properly trap and vent the line
It needs aleast a 2 in. pipe. tubs are 1.5 in.
A vent for the drain system may be blocked. A home or building plumbing system must be "free flowing" with a vent to the outside atmosphere - usually through the roof. When water is forced down the drain and the vent for that drain is blocked, air will be pulled from inside the building through another plumbing fixture causing the gurgling sound. The main drain line may also be partially blocked whereas when water is forced down the drain the air in the drain line may be forced back into the building through another plumbing fixture causing the gurgling sound.
Shouldn't be a problem. You may need to extend the pipe at the sink a bit to put in air vent so that the drain can vent. It is a checkvalve that lets in air when the sink drains. Or you can tie into the existing vent stack if possible.
Your drain waste vent is plugged or leaking somewhere. The drain waste vent is a pipe that carries sewage gas out of your home, exiting usually the roof but sometimes the side of the house. Get it fixed asap, this is not good for you.
Yes it does, otherwise it will vent in your bathroom and make everything stink. and it is not a very attractive sight to see.