Compatibility issue with PHP 5.6

Hi,
Our hosting provider is moving from php 5.3 to 5.6 and provided us a tool to check plugin compatibility. The tool generated the following 5 warnings against WPMU Dev Dashboard:

wpmudev-updates/template/support-system.php
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FOUND 0 ERRORS AND 5 WARNINGS AFFECTING 5 LINES
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77 | WARNING | Extension 'mysql_' is deprecated since PHP 5.5 - use mysqli instead.
313 | WARNING | Function name "__render_list" is discouraged; PHP has reserved all method names with a double underscore prefix for future use
334 | WARNING | Function name "__error_reporting" is discouraged; PHP has reserved all method names with a double underscore prefix for future use
376 | WARNING | Function name "__value_format" is discouraged; PHP has reserved all method names with a double underscore prefix for future use
390 | WARNING | Function name "__const_format" is discouraged; PHP has reserved all method names with a double underscore prefix for future use

Can you please confirm if it works with php 5.6 and should these warnings be ignored.
The plugin has been updated and not running an older version.

Thanks
Hasan