DTC erasure

When a DTC is thrown, it get stored so it can be read by an instrument for the appropriate fix. My question is - after the fix, does the computer recognize this and erase the code automatically or does it still have to be erased manually by the instrument? Also if the code to be repaired, is repaired, but the code is still in the system (if it is) does the computer still recognize it as a problem or not as no problem any longer exists (since the repair has been done)? Thanks in advance.

Yes the glow plug/glow plug harness will not clear. VCDS can clear it and there is a thread here that has all the people, like me, who own VCDS fka as VagCom who can help you.