Great Explanation. I don't know much about how it works, but I liked what you did and it really brought some clarity (assuming its all right

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Thanks.
At least one person appreciating it.
And yes, it is all correct. Maybe I am not 100% clear everywhere when explaining. But the text was already so long. But rest assured, the content of my explanation is all correct. It's not rocket science. I hope stuff makes sense when you read it.
So why can't we move more than one packet of data at a time?
Because that is how it works. IP technology is "packet switched". That means, data is cut in packets. And the network transmits packets one by one. The endpoints (your PC, a webserver, a game-server, etc) deals with what the packets are. Reassemble them, put them in the right order, retransmit them, etc. But you always finish one packet before you transmit the next one.
I could mention a few exceptions, but they would confuse you more than explain stuff. (ADSL can send multiple bits over different frequencies at the same time. WaveDivision Multiplexing can send multiple "colors" of light through the same fiber-strand. ATM does something with cells). But basically, all transmission technologies send one packet at a time.
What do you specifically mean by "link"?
A link is the connection between 2 routers, or between a router and a endsystem (like a pc or server). Or switches. It's more of a logical term when you look at the big picture.
A link could be ethernet, of WiFi, or fiber. Or a VPN even (if you look at it from the big picture). It's a term you can use to describe topology, without having to specify what technology you use.
Is it because there is physically a single wire that plugs into our cable modems, so each packet is going to be a represented as a bunch of well timed square waves...hence all transmission has to occur serially as opposed into parallel (i.e. such as taking advantage). Yes/no?
Yes. Kinda. As I said, different technologies have different details. But never are all bits in a packet transmitted at the same time.
Given how much lag appears to get added by the router, I would think that a good router would be able to direct the data very quickly as opposed to incurring a 100ms penalty.
The 100ms number I gave is not because the router is slow. It an example of when a router is congested. Suppose you have a home router. With one side 100Mbps Ethernet, and the other side is a 10 Mbps cable-connection. Suppose your PC sends 10 packets of size 1500 back-to-back to router. The incoming packets come in a 10 times the speed as your router can send them out. So when it has sent the first of those 10 packets, it has already received the other 9 packets. What is the router supposed to do ? It can send only 1 packet at a time. So the other 8 packets need to be buffered. And one of them can be sent after transmission is finished. After that one, the 3rd packet can be transmitted. Etc. The last of those 10 will be sent over the cable-link, quite some time after it has been received. Excuse me if I don't do the math now. But this delay is what you see when your ping goes up.
What else could the router do with incoming packets, when the outgoing link is already in use to transmit a packet ? The only alternative is to drop the packet. (Just throw it away. Drop it on the floor). That means the original sender (your PC) has to re-transmit it. And the delays there will be even bigger. And performance for the user is even worse.
Buffering is good for throughput. You can shove more data through your links. But one side effect is that delays (aka ping, aka RTT) will go up.
A solution would be to prioritize some packets over other packets. E.g. gaming-packets go to the front of the output-queue, and not to the tail of the output-queue. This is sometimes called Quality of Service. Some routers can do this. Note, for most gamers, that means that QoS actually needs to be enabled on the router owned by the ISP, that connects to your home router. Unfortunately not all ISPs do this.