HDCP (High-bandwidth Digital Content Protection) is a copy protection system used by many HDMI compatible devices. HDMI (High Definition Multimedia Interface) is the physical connection used by many video devices. HDMI 2.0 is required for 4K video. HDMI 2.1 and 2.2 add higher resolutions and more features. In general, only 4K devices have HDMI 2 ports though that may change. A 2015 HDTV with a 1080p or lower resolution display most likely uses HDMI 1.4.
All HDMI devices should be compatible. The physical HDMI connector itself is identical though some pins may not be used in lower numbered versions. When using devices with different versions of HDMI, only features supported by the lower numbered version will be used. There have been issues with HDMI incompatibility but it's not due to the HDMI version. It's because of poorly supported protocols on one of the devices. It could be caused by HDCP failure but that is not due to the HDMI version. There were more frequent reported incompatibilities with early versions of HDMI but that issue has been mostly resolved with versions 1.3 and up.
There may be issues with an HDMI 2.x source connected to a HDMI 1.x display. HDMI or HDCP failure is also possible due to a defective or poorly constructed HDMI cable. Though all well made HDMI cables are technically compatible, HDMI 2.x requires cables that are constructed to higher standards that can handle higher bandwidths.