[Q] per atom temp/profile

Is there any way to get per atom temp/profile

I would like to have kinetic tensor with spatially-averaged velocity
field extracted?

See the compute ke/atom command.
You could write a similar compute that did
the full KE tensor. You could probably also
define a variable(s) that computed the
various components. If you want to subtract
out a bias, then it would be more complicated,
but do-able with your own compute.