Will restoring from Time Machine carry over hard disk error?
The only way filesystem errors like those you describe could be copied onto a different disk (e.g. your Time Machine volume) is if the whole disk partition or whole drive were copied at the block level using dd or something like Carbon Copy Cloner.  Time Machine doesn't work that way, so its stored backups should be free from the filesystem errors and the files it restores should be free from them as well.