Can the search engine be in a different domain and network than the web/compliance search server?  Only communication from the search engine is back to the Commserve via a proxy.  Not sure if we need to put a web server in the customers environment or if they can just use our externally facing web server to run their searches.

Yes they can definitely be on different network. But there can be not firewall between WebServer and Search Engine. They should be able to talk directly. So yes WEbServer and Search Engine can be in different domain/network but the ports on which Search Engine is installed should be opened from the WebServer.

Any way to make the communication take place via firewall rules through the proxies?  These are completely different environments/networks so there are firewalls between them.

I was hoping to place the web server in the customer environment but that brings along a lot more issues with trying to get the web server to talk back to the Commserve.