Hello,
To fix the second error (and related) the plugin needs to be updated to use the MySQLi extension. (These errors could simply be suppressed, which while fast and cheap to do, doesn't actually fix anything)
The first error is strange as it would mean that no active MySQL connection could be found, unless there is a serious version mismatch between the plugin and WP, I'm sure I would be able to figure it out though.
Thanks!
Keith