I am doing tensile deformation (along z direction) simulation and want to find the longitudinal stress on the material. Is it right to use the 3rd column of the stress/atom compute and divide by the volume of the box? What will be the unit of stress in that case? According to the manual, if I am using units metal then the unit is in ‘bar’. Am I correct?

Also, how to find the indentation load for simulating nano-indentation (along z direction)? In this case, will the stress calculated in the above way and then multiplied by the xy-surface area give me load? If so, is it in units ‘bar*angstrom^2’?

No. You can access the Pzz component directly in thermodynamic output.
compute stress/atom is the subdivision of the total stress to contributions from the interaction of individual atoms with its neighbors. This way you can compute contributions of subsets by summing over all atoms within a region and then dividing by the volume of that region. There is a plethora of discussions on this subject in previous posts, so you can learn from those.