Does water from the toilet og down the same drain pipe as the water from the bathroom sink?

Yes, 99% of the time. In rare ocasions if you have a septic system, an gray water tank can be instralled and then the answer would be no.

First off you can try removing the U-trap under the sink, and see if the clog is there. You will need a good pipe wrench or Channel Lock pliers to break the nuts loose. When you get it off, you will most likely have to replace the seals, as they are most likely old and dry now, Those are cheap, and most hardware stores carry them. Just take the old ones, down and they will show you were the new ones are located. However, before you do all that work, I suggest you buy a toilet plunger or the sink plunger, also available at any hard ware store, and even in some Drug Stores and are also inexpensive. Fill up the sink, about half way, and use the power of the plunger, a few times, and hopefully, you will dislodge what is plugging up the sink. It may take a few tries, but with what you have done already, it should do the trick for you.

The answer is YES. All sinks, showers & toilets & even your washing machine drain to the main sewer line in your house that goes to the sewer in the street. & NO you can NOT get sewer water out of a faucet. Completely different piping all togeather.

Also most of those thumbs downs are correct answers too.

My house built in 1970 has the toilet water go down into the septic tank and all other waste (bathtoom sink, dishwasher, etc) goes into a hole on the other side of the house, filled with rocks. I don't think this is legal anymore because of so much development. I still have 100 acres of woodland around my house so I don't worry about if! (and it's grandfathered in). So I guess my answer is ... it depends on your house.

Yes! Unless you design your own house and specify to the builders that you want separate drains, they will all eventually link up to one drain pipe. This is easier and necessary for the city when they have to repair or do any remodeling for zoning. Contractors are able to look at the blueprint design and quickly known where one primary pipe is located, as opposed to several separate drain pipes.

eventually

Every Drain in your home eventually meets up into the same 4" piece of pipe, then goes into the septic system.

Both drains go into the same waste line.

Before you waste alot of time and/or money on the invention be sure and check the plumbing codes to see if it would be allowed.

Yes, they all end up in the same pipe.

The toilet drain pipe is larger than the sink, shower, tub and laundry drains. the smaller drains collect into the larger toilet drain, then all drains eventually collect into one drain that goes out to the street (or septic tank).

Almost exclusively, yes. One in, one out for each household. Many sewer systems also combine rainwater with household waster further down the line.