What is the relationship between NP/NP-Complete/NP-Hard to time complexity?
See the definition of NP completeness. For a problem to be NP-complete, it 


needs to be in NP and 
all NP problems need to be reducible to it in polynomial time. 


Condition 2 alone is what it means to be NP hard. Thus NP complete problems are the intersection of NP problems and NP hard problems.

NP $\subseteq$ EXPTIME, thus NP problems can be solved in $2^{O(p(n))}$, for some polynomial $p(n)$. But it is well know that if P $=$ NP, then NP problems can be solved in polynomial time. 

NP hard problems are at least as hard as NP problems – you cite a few examples.