To answer your second question, ADS 11.1 is planned to be supported until December of 2016.
In regards to the client, you should be able to update the server and leave the clients at the older version (minimize change). The server is backwards compatible with older clients. However, I would suggest full testing on a DEV system to ensure compatibility for your specific application.
As for the server question of being able to run both at the same time. This is possible, but likely more hassle than worth the time.
In general I would recommend an upgrade of the old version to the new version. If you find issues you can uninstall the new version and re-install the old version. To be safe, take screenshots of the server config or export the registry prior to upgrade \\HKEY_LOCAL_MACHINE\System\CurrentControlSet\Services\Advantage\Configuration
If you would like to run both at the same time or have both installed you can look at side-by-side install, however each will run on a different port and have separate settings, etc. Also you can not open the same database in both versions at the same time.