For the planning part of your post:
Our group has a lot of variation in when they have to work which makes scheduling hard. So we started to use this tool: You just create a dudle and ask anyone to fill it out and then you can easily see when you guys would be able to play.
You should check https://dudle.inf.tu-dresden.de/?lang=en, https://terminplaner4.dfn.de/ and https://poll.digitalcourage.de/. The php script seems to be the same on DFN and digitalcourage site, so I guess some php scripts exist that you might host yourself. My webspace provider offers LimeSurvey (php poll script) scripted installation, easy enough. If you trust your provider better than Google, this is the most privacy-centric alternative. If you don't have the possibility to install and publish the script on a machine you administrate which is of course best.
By better I really should have specified FOSS, as this is what /u/lookindandy seemed to be concerned about.
Dudle (AGPL)
Limesurvey (GPL)