I have read that TSP and Subset Sum problems are NPC problems which are also NP Hard. There are also problems like Halting Problem which is NP Hard, but not NP Complete
And Wikipedia defines this as
A problem $H$ is NP-hard if and only if there is an NP-complete problem $L$ that is polynomial time Turing-reducible to $H$.
Like NP Complete problem is there any problem considered to be the first NP Hard problem?
To show one problem to be NP Hard we need just to reduce one NPC problem to it?
Whether all NPC problems are NP Hard?
If no, why not?