Please edit the file component/site/views/YOUR_JEVENTS_THEME/month/tmpl/calendar_cell.php and search for this code
$dom->loadHTML($cellString);
See
https://github.com/JEvents/JEvents/commit/6b0e5d6e16b74dc511b6458f311865f44ff1ae13 for the relevant line numbers, and change it to
$dom->loadHTML('<html><head><meta content="text/html; charset=utf-8" http-equiv="Content-Type"></head><body>'.$cellString.'</body>');
This should resolve the issue with non-ascii characters in the tooltips. Once you have confirmed this resolves your issue I'll release JEvents 3.4.29 with the fix inculded.
For your returning to May 2016 issue - I would suggest you switch off the new SEF URLs in the JEvents config (SEF/Performance tab). This will include the day/month/year values in the event detail URL and may resolve this for you. This is not ideal for SEF purposes since it generates lots of very similar URLs for the same event detail page and makes the URLs less readable.