Yes, the Panasonic Eluga Ray 500 does have a fingerprint sensor with it. Getting a fingerprint sensor at its price range is quite a good deal.
Its fingerprint sensor is located at the front on the HOME button.
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Yes, the Panasonic Eluga Ray 500 does have the screencasting feature. In fact, all the smartphones above Android 4.4 KitKat have had this feature.
To open this feature, you can go to settings and then to connected devices and then to cast. It was for the Android Oreo phone, but anyway the procedure would be quite same.
Check full device specifications Panasonic Eluga Ray 500