What you observe is quite normal:

> Then I copy it to a new session and create a supercell 2X2X1 with
lattice F. The program recognizes 8 inequivalent atoms, each with two
positions (total of 16 atoms).

Correct. Four atoms in the original cell, multiplied by 4 (=2x2x1), and then divided by 4 (F-symmetry) makes 16.

Then I replace the last atom of Se by Te
so that I have a doping of 25% and set its RMT to 2 and the atomic
number to 52. RMT_Fe=2.1 and RMT_Se=1.96.

Setting the RMTs manually is not needed, unless you have specific reasons for doing so. setrmt_lapw will make a faire choice later on, during the initialization (or by the 'do this at least once' step in the structeditor if you use w2web).

Here I have a couple of
questions. First, I wonder if we have to label all inequivalent atoms
(for instance, Fe1, Fe2, Se1, Se2, etc.)

No. After x supercell and replacing, the structure file does not yet contain the proper symmetry information. The atoms at are their correct positions, but not yet correctly grouped into blocks of equivalent atoms. If you label now, you'll end up with less symmetry than you could have.

because when I compute xnn, I
got a warning like this

  WARNING: Mult not equal. PLEASE CHECK outputnn-file
  WARNING: ityp not equal. PLEASE CHECK outputnn-file
  WARNING: ityp not equal. PLEASE CHECK outputnn-file

   NN created a new SFeSeTe.struct_nn file
NN created a new CASE.STRUCT_NN FILE
0.016u 0.000s 0:00.01 100.0%    0+0k 0+160io 0pf+0w

That is due to the above-mentioned reason. And nn even suggests an improved structure file for you, as it tells: case.struct_nn. Hence, replace case.struct by this case.struct_nn, and proceed with sgroup.

If I continue to x group I got another warning such as this:

warning: !!! Number of inequivalent atoms has changed. !!! Old value= 8
New value= 6 warning: !!! Bravais lattice has changed.
sgroup found: 12 (C 2/m) [unique axis c] cell choice 2

Why? And then the program suggests to change the sgroup. If I don't
accept and continue I get an error in editinst step:

Similarly as nn, sgroup suggests you a file with the correct symmetry (sgroup is even smarter than nn, and could further improve the suggestion by nn). Accept its suggestion.

Stefaan
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