Hello,
JEvents 3.4 now uses the official Joomla! JQuery/bootstrap library. Opposed to the previous Joomla! Moo tools library.
In regards to the styling you can configure what versions of bootstrap JEvents loads in the JEvents config.
In regards to the map plugin, It sounds like a possible jQuery conflict. But again we use the official Joomla! JQuery library and or Google maps plugin works perfectly so interacts with the Google Api fine.
You might want to ask the developer for support on that one.
Many thanks
Tony