LazaruX, only an old obsolete part was removed from Lazarus. By installing the "weblaz" package you will be able to build CGI/FCGI(FastCGI) and Apache modules using fpweb/fcl-web.
Additionally, there is the "lazwebextra" package which adds suport for ExtJS, etc.
Herux, yes I believe it is possible to do http server push with Lazarus/FPC . The best would be if you ask about this on the FPC developers mailing list, unless someone posts some more details here on how to do it.