Hi,
I don't have the problem on my local test server with the exact same settings.
I think there is something else going on on your end. For example, a problem with how time zones are configured.
In the settings of the date picker plugin, there is a setting "Set hour to noon when processing time" which you can activate so that the plugin will use noon instead of midnight for the time of the date. This should help prevent time zone issues, so I would recommend activating this option.
Regarding the deprecated messages, thanks for your feedback. We'll add a patch for that in the next version. You can ignore them for now.