Why does the bathroom sink back up into the tub

Why does the water from bathroom sink back up into bathtub? Thanks!

I just very proudly finished installing our new second floor bathroom sink drains. Two different vanities, two different walls. I ran the water steadily in both of them for 10 minutes. One works fine. The other backs up about halfway up the bowl, then suddenly quickly drains everything and...

I had a clog in the pipes under my bathroom sink. I shut off the hot and cold water valves before removing the pipes (just in case someone accidentally turned the water on while working). I ended up replacing the pipes and got everything set up. I turned the water valves back on but, when I turn...

The main bathroom sink and tub drain really slow. I thought I corrected the problem a couple of months ago by taking the trap off of my sink and using a small snake to unclog the pipes. It worked, or so I thought. Now I have the same problem. It is only these two drains. Do I try the snake...

There has developed, in the last week, a "fog horn" sound when we turn on the hot or cold taps in the bathroom or kitchen. It does not occur when we use the washer or dishwasher. Could anyone give some advise on what could be the cause of this?