Ip – When a datagram moves through a network, do the MAC or IP addresses change

I understand that when data is sent to another network, it has to use logical addresses, or IP addresses, to get there

Like the moderator said, IP and mac addresses are used on ethernet, so you are confused and don't understand how this works. If a PC-A on ethernet sends IPv4 traffic to an PC-B on another network, the packet still needs to arrive at the first-hop router. The destination IP address will be PC-B, but the destination mac-address is the first-hop router's mac.

PC-A is configured with the next-hop router IP address and PC-A ARPs to find the mac address of the first-hop router.

In this case, the first-hop router (also called the "default gateway") uses its routing table to find the proper interface to deliver the packet towards PC-B.

what if the destination for the data is on the local network? Do they use IP or MAC with ARP, and is that Layer 3 or 2? Like, is the Network layer used at all if the destination is on the local network?

If PC-A wants to send IPv4 traffic to PC-C on a local network, both the destination mac-address and the destination IP address are for PC-C.

PC-A realizes that PC-C is on the same network, so it ARPs to find the mac address of PC-C.

In this case, the lan-switch uses its mac-address table to find the proper interface to deliver the packet. However, PC-C still checks the destination IP address to ensure it belongs on PC-C.

First off - your English appears to me to be excellent. Secondly your summation of bridging (question 1) and consequently your understanding of the subject are very good. I would probably word some of that slightly different but your summation is fair and it appears that your understanding is good.

Let's make one assumption at this point to keep things simple - this is all Ethernet and IP.

Having said that there are two steps that I would add to your bridging summation that might clear up your understanding of routing (question 2) a little:

1. when your network stack is handed data to transmit there is a route table look up done (every device on an IP network contains a route table - to see it from a command prompt - on linux type "route", on windows type "route print".) to determine two things:

a) which interface to transmit the data out

b) if the destination is directly reachable or is remote (beyond a router).

2. Once the route is determined the network stack will ARP for a MAC address.

So when Alice is sending data to Charlie she does a route lookup - it is determined that his machine is directly accessible on the LAN. She then ARPs for his MAC address. Once the route has been determined and the MAC address has been acquired the network stack can then assemble the packet for transmission. This particular conversation as you mentioned only traverses switch A as it inspects the destination MAC.

Now that we have fleshed out question one a little better let's apply some of these concepts to question 2.

When Alice desires to send data to Bob the first step is a route lookup. It is determined that Bob is not on the LAN. Thus the route to Bob is the default route (assuming Router A is configured as such). (As your book points out Router A - and by extension Alice - don't know where Bob is. They only know the general direction - or "route".) So Alice ARPs for Router A. Then assembles the packet with destination IP address(network layer) of Bob and MAC address(datalink layer) of Router A. Upon receiving this packet Router A 1)strips off the MAC address(datalink layer) of Alice 2)does a route lookup 3)ARPs for router B 4)then reassembles the packet with MAC address of Router B. Router B repeats these steps ARPing for Bob and forwards the packet.

So the network layer is assembled at the start - source Alice and destination Bob - and never changes. The datalink layer on the other hand is deleted and reassembled each and every leg of the trip.