I have noticed that the rear brake pad touches the tire slightly. I have moved the brake pad all the way down. But it did not go any further down, and the pad is still touching the tire. I have tried to turn caliper but after I brake it does not fully opened.
Do you know how to fix it?

What kind of brake is it? Since this is the road forum, I will presume a sidepull. You probably need to center the brake caliper. Depending on the brake style there are several ways it might be done:

-Allen head in the top middle of the brake arm
-Flats on the side of the brake bolt, behind the brake. There is a special wrench to fit these narrow flats.
-If neither of the above, you will need to use a tool to rotate the brake calipers by the return springs. There is also a wrench you can buy that fits into the loops of the spring to make this job easier.

Was this brake ever working correctly, or is this a build of some cobbled-together parts? There are road frames (generally ones that are designed to accommodate fenders) that require long-reach brakes.

A picture would help.

May be a wheel size issue too. I'm not sure, but would a 650c wheel on a 700c frame result in this?

Thanks for your replies. The issue of not retracting left "arm" is solved. It was a tiny hex screw that fixes the brakes on the pivot. The screw was loose, I did not noticed that, because I did not know how deep it should be in.

But, there is another problem of brake pads slightly touching the tire although the pads are on the lowest point. LBS says that my new wheels with Kinlin 700c rims will not work with my brakes. I have stock Cannondale C4 brakes on my CAAD8.

They suggested to buy new rear brake calipers with deeper reach. I cannot find specification on reach on my current C4 brakes, is it 39-49mm or 37-47mm? There are several models with long reach like Shimano R450 or Tektro R730. The LBS says they should be compatible with my Tiagra shifters with Shimano Super SLR pull.

Is it normal that Kinlin rims will not work with normal short reach brake calipers?

Should I buy just rear brake or the set? Shimano or Tektro? Any recommendations on model will be appreciated. Thanks!

The rims themselves should have nothing to do with needing long or short-reach brakes. The need for long-reach is usually determined by the frame -- i.e., some frames have the brake mounted "high" in order to provide clearance for bigger tires / fenders, and thus require a long reach brake.

Do you have a large tire mounted on the rims? i.e., a 700x28 tire on a road bike can be a really tight squeeze (no pun intended). I'm not familair with the C4 brakes, but I guess it's possible that they don't have the reach to get around a "larger" tire.

Long vs. short reach brakes work with the same brake levers. I had the Tektro R730's on a bike at one point; they worked fine.

my tires are 700x23, nothing special