Enthalpy change defined at constant pressure only?
Is change in enthalpy defined only at constant pressure?


No. The definition of $\Delta H$ is $\Delta H = \Delta U + \Delta (PV)$  Simple as that.


  I know Q-W=del(U) And Q at constant pressure equals del(H) (enthalpy
  change).
  
  Can Q (heat given to the system) be used interchangeably with del(H) in the first equation?


No.  Only if the applied pressure is held constant during the change.


  Is del(H) =nCp del(T)? How?


No.  Only for an ideal gas.  For real gases, this equation is not correct outside the limit of ideal gas behavior.  For an ideal gas, $\Delta U=nCv\Delta T$ and $\Delta (PV)=nR\Delta T$, so $\Delta H=n(C_V+R)\Delta T$.  And then $C_p=(\partial H/\partial T)_P=C_v+R$, so $\Delta H=nC_P\Delta T$.  

For a real gas, liquid, or solid,
$$dH=nC_PdT+\left[V-T\left(\frac{\partial V}{dT}\right)_P\right]dP$$
Note that the term in brackets is zero for an ideal gas.