When we try to run the command (principle no matter what, let it be ls-la) (para 4)
are there any additional checks on the server from the security point of view?
No. The user accessing the ssh is no different from a normal local user.
Can someone tell me which algorithm you run the command on the remote machine? (Assuming that we are already connected to the server).
Just look in the output of pstree:
├─sshd(700)─┬─sshd(8208)───sshd(8214,jcmvbkbc)───bash(8215)───ssh(8231) │ └─sshd(8232)───sshd(8238,jcmvbkbc)───bash(8239)───pstree(8244)
to understand that after you connect via ssh, sshd (the ssh daemon, the process 8238) launches a login-shell (process 8239), which shows the prompt ($). When it is typed in the command pstree (process 8244), shell simply runs this command.