Change in IP header length

You're right UDP header is 8 bytes. So I can't really explain your 12+8 scenario. Pseudoheader refers to the header which is considered when calculating checksum, is is combination of IP + UDP + payload, but not all of if, hence pseudo.

20B is normal size for IPV4 (and TCP). So maybe confusion lies there?

If you can put your example online, it might help understanding what the author tries to communicate.

EDIT the packet you entered is 20+8+13 bytes. If your document claims 20+13, it is missing the UDP header.

MAC addresses are layer-2 addresses in the frame header. The layer-2 frame encapsulates the layer-3 IP packet. The layer-2 frame is stripped off at a layer-2/3 boundary (e.g. a router). If the layer-3 packet needs to be forwarded through another layer-2 domain, a new layer-2 frame is created using MAC addresses in the new layer-2 domain to encapsulate the layer-3 packet.

Conceptually:

To the router:

<L2 frame><L3 packet><L4 segment>PAYLOAD DATA</L4 segment></L3 packet></L2 frame>

In the router:

<L3 packet><L4 segment>PAYLOAD DATA</L4 segment></L3 packet>

From the router:

<New L2 frame><L3 packet><L4 segment>PAYLOAD DATA</L4 segment></L3 packet></New L2 frame>

The original layer-2 frame will contain the source MAC address of the sender, and the destination MAC address of the router's interface in that layer-2 domain.

The new layer-2 frame will contain the source MAC address of the router's interface in the new layer-2 domain, and the destination MAC address of the next hop in the new layer-2 domain.

The layer-3 packet will contain the layer-3 source IP address of the originator of the packet, and the layer-3 destination address of the final layer-3 destination.

Layer-2 MAC addresses are removed at each layer2/3 boundary along the routes to be replaced with the MAC addresses of the new source and destination, but the layer-3 IP addresses stay the same along the path (with certain exceptions like NAT).