"Is it possible to run a sas program (.egp file) developed in EG on a Unix SAS system?"
I would think if the code runs out of EG on this SAS Server under Unix then the exported code should also run in the same environment.
You might have to check that the users used to run the code are in the same group (i.e. SAS EG might use sassrv as Unix user but when running the same jobs as .sas file the user might be your user or "sas") - or that at least all necessary permissions are set for the user to run the .sas file.
You might also have to make sure that the EG maco library is also available for the user running the .sas file.
"why is the sas syntax in .egp file(when exported to sas file) looks very different than the usual SAS coding?"
What do you mean by that? Are you talking about this pre- and post-code "crap" EG adds to code - or are you talking about the "body" code as such? And what is "usual SAS coding"?