I have been trying to understand MetaRouter, and I have some questions.

1. Seeing as OpenWRT contains php, apache, etc, am I correct in thinking this could be used as a web server for using with the API on the main router? ...instead of needing an external server?

2. In that same light, I assume then it would also be possible to use the same MetaRouter to run squid/privoxy/tinyproxy. In the main router's proxy settings, you would then set parent-proxy to the IP of your metarouter.

Am I thinking correctly?

What you are thinking should work.

Just make sure metarouter is supported on your hardware.