What all fields is the FCS/CRC in the trailer of the ethernet frame calculated over?
Check IEEE 802.3 Clause 3.2.9:
This value is computed as a function of the contents of the protected
fields of the MAC frame: the Destination Address, Source Address,
Length/ Type field, MAC Client Data, and Pad (that is, all fields
The source/destination address of the frame changes at every hop.
The frame (including MAC source and destination addresses) does not change across L2 hops. For an L3 hop (router), the frame containing the MAC addresses doesn't survive the hop. Instead, the router decapsulates the contained L3/IP packet, makes its forwarding decision and (if necessary) re-encapsulates the packet in a new frame built for the egress segment.
Also, the IP header TTL is modified by en route routers.
That's true. Note however, that the IP header is a part of the L3 packet.
With so many changes happening, how can the primary sender set the FCS and the end receiver discard the final frame based on the CRC/FCS failure?
The primary sender builds the IP packet including the header checksum (for IPv4). For an Ethernet network, the IP packet is encapsulated in an Ethernet frame including the calculated FCS. The frame doesn't change across the switches on its path until the first router is reached, where the frame is discarded.
The final IP destination checks the FCS from the frame built by its local gateway, extracts the IP packet, checks its header checksum (for v4) and extracts its payload, often with its own checksum.
Since the IPv4 header checksum is pretty much redundant and the continuous TTL change and the checksum recalculation puts load on the router, the checksum has been removed for IPv6.