Somewhere I read that copying data from HDD having bad sector, can copy bad sector too and may corrupt health HDD.
No, this is not true. However, you can end up with corrupted data, since the data wasn't recoverable from the original drive.
When a drive has a bad sector, the drive firmware uses various tricks to try to recover the data (flying closer to the disk, increasing the tolerance on the signal detection system, simply trying to read it a dozen times and hoping one of them works, etc), only if all of that fails... the drive reports an error back to the operating system.
What happens now depends on which knobs the operating system has turned. The drive typically tries to blacklist that sector and returns some pregenerated data (usually 0's, although this is configurable) back to the computer. For subsequent writes to that location, the drive internally remaps those sector addresses (LBAs) to a special section of the drive dedicated to such things.
Most hard drive errors are never seen by the user, since modern drives are fairly good at recovering data on their own. Some types of drive errors, such as bumps on the surface of the disk or damaged heads... have a tendancy of "spreading" across the drive. Causing you to lose more and more data as time goes on. If you are seeing errors persistently, you should be getting rid of that disk quickly... since you may have filled that section of the drive used for overprovisioning, or simply have ALOT of errors.