Besides accessing your page are random people able to use your server as an exit node? Am I thinking the right thing... I met someone in Switzerland that was hosting anonymous exit nodes to some anonymous network and he said that it was a pain having to explain what was happening to the police.

Exit node are an entirely optional part of the Tor network. If you run a relay or a hidden service you are not forced to participate in the exit node side of things. It's also not recommended to combine these roles because it could have security implications for your hidden service.

Running a Tor exit node is a manual process. Running a hidden service like a website, or chat server doesn't involve anything like that.

That'd be an exit relay, not doing that atm, just in case

No