Made Monitor not affect "Who'se online", logged API methods and removed previousGameId from URL

Resolves #1154.
Resolves #271.
Resolves #1161.

http://jenkins.buttonweavers.com:8080/job/buttonmen-AdmiralJota/397/

I put #1154 and #271 in the same pull request since they both touch some of the same files and seemed likely to conflict with each other otherwise (and because I had naively expected them both to be small changes). I threw in #1161 because it's just one extra line that I had put in *anyway* to test out a method I wrote for #1154, and it seemed silly to take it back out again.

To test the API method logging, I put this into my local Apache config:

    LogFormat "%h %l %u %t \"%r\" %>s %b %{BMApiMethod}n %{BMUserID}n" common

...and that worked fine.