C13 to C14 compatibility

Yes: C13 is made to mate with C14. That is the standard 10 A jumper used on most 1U/2U PSUs.

No: C13 does not mate with C20. If the inlet is C20, you need C19, not C13.

No: plugging C13 into a C14 inlet does not turn the circuit into 16 A. Stay at the nameplate current (often 10 A on Dell C13/C14 jumpers).