The web server is a node application and you can find it at: /usr/lib/edison_config_tools/edison-config-server.js. If you want to disable it, I would suggest you to check this thread How do you disable the default Edison server?, where this is explained with more detail.
About sqlite, you can use the AlexT repository to install this software, http://alextgalileo.altervista.org/edison-package-repo-configuration-instructions.html.
The website above contains the necessary configuration for the Edison to add packages from the repo. The sqlite package can be found in here http://repo.opkg.net/edison/repo/core2-32/.
re PHP: I used lighttpd in the past with mod_php. Works fine. You should find the packages also at AlexT's repo if you want to give it a try