yes.
Take your snake on the roof and clean the drain from the vent.
The vent for the drain is in the wall. Where the drain goes in, it T's with the water going down and the vent going through the roof. With a double sink, one side is the vent for the other. As long as the water isn't pulling against a vacuum, it will drain.
If the drain is used as a wet vent for another fixture 2". Otherwise 1.5".
By properly sizing the vent by fixture units and developed lengh and pitching it up from the fixture it serves
Make sure the drain line and the vent are cleared. Noises like that are usually caused by either restricted flow or a plugged drain vent.
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
This would not be a good idea because if you get any back draft which is likely when the vent isn't working then you have one smelly bathroom.
You have a blockage in your main sewerline. You have a problem with your venting system. This is why some codes now require a vent within 6" of the toilet. If you will add a vvent to your main line at the toilet you will stop this. Check to make sure your vents are not clogged by a bird or bees nest first.
vent in bathroom manditory
your vent on your shower or kitchen (if you have one) is not working and either the air from the water in the shower drain is carried down stream till it T's off to your kitchen sink then the air follows to your kitchen sink drain line backwards and to your kitchen sink trap and then bubbles through your trap because your water in your kitchen trap can not drain but the air has enough pressure to go through it OR your water from your shower is flowing past your kitchen drain T and making a siphon which causes air to go through your kitchen trap and makes the gurgling sound one way to fix the problem is to add a Vent line on your kitchen drain and your shower drain with in 42" on 1 1/2 or 60" on 2" on your trap arm if you want to follow the UPC code. Note to above Respondent: That little dot next to the question mark is a "period". Try throwing one in once in a while.
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.