The DK-5 eyepiece cover should have been provided with the camera when it was purchased. However, it is fairly inexpensive and can be purchased here.

The D5200 does not have a panorama setting and there is no way to add it to the device. Nikon has an article about creating panoramic shots that outlines how to create a panoramic shot here.

The D5200 can take pictures at preset intervals and be put together in your editing software to create a time lapse effect. To access the settings, press the "menu" button, scroll to "shooting menu", and scroll to "interval timer shooting". In this menu you can choose when you want the interval shooting to start, how fast you want the pictures to capture, and how many frames you would like to capture. PhotoRec Toby has a short video describing this feature here.