This may be obvious, but for the new version release 3.2 do I need to install BOTH the Events calendar and The Pro version updates? And I suppose the Events free version first, then the Pro version?
Yes: please do ensure they are kept in synch, so The Events Calendar 3.2 and Events Calendar PRO 3.2 should be paired together (if you do not, a warning notice should display informing you of this).
If you have entered your license key then you should be able to leverage automated updates here – simply visit the plugins admin page, check the entries for The Events Calendar and Events Calendar PRO and update.
There is indeed a bug (actually it stems from an issue with tags). However, this snippet which can be added to your theme’s functions.php file ought to resolve it until the subsequent release arrives with a definitive fix.