First, I would recommend performing a reset. To do this, hold down the Power/Lock key for 10 seconds until your device restarts and you see the BlackBerry 10 OS loading screen appear (with the BlackBerry logo and progress indicator). See if the issues persist.
If this does not resolve it, I would perform a device software reload, either via BlackBerry Link or using an autoloader. Create a backup of your device first as either method will erase any data you have on your phone. Once the software has been reloaded, complete the initial set up process and test to see if the slow performance and rotation lock issue persists. If not, go ahead and restore your backup and once the device restarts see if things are still working okay. If things start acting odd after restoring the backup then I would advise performing a security wipe or another reload, at which point set things up again manually as there may be something in the backup that is causing the issue to occur.