Yeah, for this, I started with this and this. With that said, it's still mostly arcane witchcraft. 🤣

Of course not, but I've found that seeing the protocols in action and looking at real headers can be very helpful in making them click. Understanding DHCP or ARP or mDNS or BGP or whatever is much easier by inspecting a pcap than it is by reading RFCs

The tcpdumps I've worked with can also dump UDP, ICMP, and even ARP.

Yes, but before I used it I assumed that its scope was pretty much limited to what you just mentioned. Instead it can operate on most protocols both above and below layer 4, and it is incredibly useful as a traffic capture tool to produce a .pcap on a remote headless machine which you can then load into Wireshark. The "dump" part is the interesting one, not the "tcp" ;)

Yes. Also learn about certs if you need to deal with encryption https etc.

Electrical engineering is just layer 1 on the OSI model.