1) 

For 2D graphene I find the following dependence on the 2D stress tensor (directory is vacuum in Ang)

100/RUN.out:siesta: 2D stress tensor (static) (eV/Ang**2):
100/RUN.out-siesta:       -0.104105      -0.000000       0.000000
100/RUN.out-siesta:       -0.000000      -0.104441       0.000000
--
110/RUN.out:siesta: 2D stress tensor (static) (eV/Ang**2):
110/RUN.out-siesta:       -0.104470      -0.000000       0.000000
110/RUN.out-siesta:       -0.000000      -0.104806       0.000000
--
120/RUN.out:siesta: 2D stress tensor (static) (eV/Ang**2):
120/RUN.out-siesta:       -0.104281      -0.000000       0.000000
120/RUN.out-siesta:        0.000000      -0.104617       0.000000
--
130/RUN.out:siesta: 2D stress tensor (static) (eV/Ang**2):
130/RUN.out-siesta:       -0.104602      -0.000000       0.000000
130/RUN.out-siesta:       -0.000000      -0.104938       0.000000
--
20/RUN.out:siesta: 2D stress tensor (static) (eV/Ang**2):
20/RUN.out-siesta:       -0.104098      -0.000000       0.000000
20/RUN.out-siesta:        0.000000      -0.104434       0.000000
--
30/RUN.out:siesta: 2D stress tensor (static) (eV/Ang**2):
30/RUN.out-siesta:       -0.105210      -0.000000       0.000000
30/RUN.out-siesta:       -0.000000      -0.105546       0.000000
--
40/RUN.out:siesta: 2D stress tensor (static) (eV/Ang**2):
40/RUN.out-siesta:       -0.104277       0.000000       0.000000
40/RUN.out-siesta:        0.000000      -0.104613       0.000000
--
50/RUN.out:siesta: 2D stress tensor (static) (eV/Ang**2):
50/RUN.out-siesta:       -0.105209       0.000000       0.000000
50/RUN.out-siesta:        0.000000      -0.105545       0.000000
--
60/RUN.out:siesta: 2D stress tensor (static) (eV/Ang**2):
60/RUN.out-siesta:       -0.104109      -0.000000       0.000000
60/RUN.out-siesta:       -0.000000      -0.104445       0.000000
--
70/RUN.out:siesta: 2D stress tensor (static) (eV/Ang**2):
70/RUN.out-siesta:       -0.104656       0.000000       0.000000
70/RUN.out-siesta:        0.000000      -0.104992       0.000000
--
80/RUN.out:siesta: 2D stress tensor (static) (eV/Ang**2):
80/RUN.out-siesta:       -0.104286      -0.000000       0.000000
80/RUN.out-siesta:        0.000000      -0.104622       0.000000
--
90/RUN.out:siesta: 2D stress tensor (static) (eV/Ang**2):
90/RUN.out-siesta:       -0.105208       0.000000       0.000000
90/RUN.out-siesta:        0.000000      -0.105544       0.000000


For a 1D carbon chain with directory being the vacuum along the two perpendicular directions
10/RUN.out:siesta: 1D stress tensor (static) (eV/Ang):
10/RUN.out-siesta:        0.000000       0.000000       0.000000
10/RUN.out-siesta:        0.000000       0.000000       0.000000
10/RUN.out-siesta:        0.000000       0.000000       7.196726
--
20/RUN.out:siesta: 1D stress tensor (static) (eV/Ang):
20/RUN.out-siesta:        0.000000       0.000000       0.000000
20/RUN.out-siesta:        0.000000       0.000000       0.000000
20/RUN.out-siesta:        0.000000       0.000000       7.198956
--
30/RUN.out:siesta: 1D stress tensor (static) (eV/Ang):
30/RUN.out-siesta:        0.000000       0.000000       0.000000
30/RUN.out-siesta:        0.000000       0.000000       0.000000
30/RUN.out-siesta:        0.000000       0.000000       7.196728
--
40/RUN.out:siesta: 1D stress tensor (static) (eV/Ang):
40/RUN.out-siesta:        0.000000       0.000000       0.000000
40/RUN.out-siesta:        0.000000       0.000000       0.000000
40/RUN.out-siesta:        0.000000       0.000000       7.206712
--
50/RUN.out:siesta: 1D stress tensor (static) (eV/Ang):
50/RUN.out-siesta:        0.000000       0.000000       0.000000
50/RUN.out-siesta:        0.000000       0.000000       0.000000
50/RUN.out-siesta:        0.000000       0.000000       7.196725
--
60/RUN.out:siesta: 1D stress tensor (static) (eV/Ang):
60/RUN.out-siesta:        0.000000       0.000000       0.000000
60/RUN.out-siesta:        0.000000       0.000000       0.000000
60/RUN.out-siesta:        0.000000       0.000000       7.198949
--
70/RUN.out:siesta: 1D stress tensor (static) (eV/Ang):
70/RUN.out-siesta:        0.000000       0.000000       0.000000
70/RUN.out-siesta:        0.000000       0.000000       0.000000
70/RUN.out-siesta:        0.000000       0.000000       7.211712


It is relatively stable but is dependent on the mesh and eggbox (here 400 Ry).

2) No, true. It is not an explicit equation for a slab. So I don't know if we should name it differently? "1/2D stress tensor (approximated) (static)"? or?