Your problem for the push is authentication.. the phone doesn't authentiate a push request.. instead it sends the credentials to the authentication url defined in the phone. So, you'd need to configure the authentication url to go to one of your one pages, which returns the appropriate response when the phone asks (I don't recall.. I believe it returns "AUTHORIZED" when the authentication is okay.. just sniff the http traffic between a phone and the CCM when you run the app on the CCM so you know what your custom authentication page has to return). That's really the only difference for pushing on the CCM and CME.

AXL can be used, however, only a subset is available. For more information on what commands you can use, go to http://www.cisco.com/cgi-bin/dev_support/access_level/product_support and select Call Manager Express from the dropdown. Here's a direct link to some documentation (they call the whole thing "Router XML"): http://www.cisco.com/univercd/cc/td/doc/product/voice/its/xmldev.htm

"Can I develop only one code and run to all Cisco call manager ? "

As you can see from the documentation I linked to, this is a resounding no. A CME runs on a router and hence is configured like a router. AXL is basically an IIS filter sitting on the call manager, translating XML documents into SQL statements, executing and returning them. Since there's no SQL on a router, you cannot expect the same commands to work.