A slow draining washroom sink is usually the result of hair in the drain line. I recommend taking the trap apart if possible. Remember it should be full of water. Next take needle nose pliers and try to pull out the obstruction. If there is nothing in the drain your problem could be a poor venting. Water will not drain well unless it has a supply of air to allow it to move down the drain. Think of venting like holding your finger over the top of a straw full of pop. Until you release your finger the pop stays in the straw. If the problem is venting you will hear a gurgling noise and see bubbles when the water is draining. The smell you describe sounds like a vent problem. When the venting is wrong you can sometimes suck the trap dry causing sewer gases to come back into the sink. I recommend hiring a plumber if you cannot figure out the issue.