I'm unable to provide diagrams, but I can describe a sink P-trap for you. A sink P-trap is a curved pipe located under the sink that traps water to prevent sewer gases from entering the house. It has a U-shaped bend that holds water to create a seal. This seal prevents odors and gases from coming back up the drain.
You usually have to unmount it and get at the bottom.
The shape of the drain. A P trap drains out the wall. It looks like a P laid on it's side. An S trap drains in the floor. Again if you laid the S on it's side.
Probably rust and minerals that came loose when you turned the water off and plugged the screen in the spout. Unscrew the screen the the end of the spout and see if that doesn't fix it.