how to publish build code in eclipse(which is in my local system) to web sphere in server
Read the documentation: http://www.ibm.com/support/knowledgecenter/SSHS8R_7.1.0/com.ibm.worklight.installconfig.doc/install_config/c_wlserver_plan_install.html?lang=en
The build in the MobileFirst development environment in Eclipse generates .wlapp, .adapter and .war files. You need to setup a production environment (must be a licensed customer of IBM) and then follow the instructions in the guide above in order to first deploy the the server artifacts -> the .war file -> and then the .wlapp and .adapter files.
What are the minimum required software's that are required in server to publish
See the Prerequisites website: http://www-01.ibm.com/support/docview.wss?uid=swg27024838#IMF_71
Is it possible to publish code in server without eclipse in server, If so can I know how to do that.
You must first build the required artifacts. This must be done using either MobileFirst Studio or MobileFirst CLI.