You have a broken or clogged line beyond where the sink pipe is attached. You may also have a full septic system if you are on septic. It is now leaking from the bottom of the toilet probably due to using the plunger and the pressure not having anywhere to go or a moving of the toilet doing so. It also sounds as if the system may not be vented. You can rent or borrow a snake, remove the toilet and snake it yourself much cheaper than a contractor will do it for. Make sure you get one that will do 3″ and 4″ pipe size. You’ll need a new wax ring and toilet hold down bolts if you do it. They are available at Home Depot and sold as one unit. You may possibly need a new water supply tube if the old one won’t work. You’re looking at probably 70 to 80 dollars for rental and materials vs a few hundred if a plumber does the work. I hope this helps.