They're what is called federated. They use the same protocols which allow each to see the other. The best comparison I've heard to describe it is like how you can read emails irrespective if someone used Google Mail, Yahoo Mail, or Microsoft Outlook, or whatever email sending software.
Simply put, the difference between a protocol and an API are that a protocol is how you communicate, while an API is a way for software to not just communicate with a server but get it to do things as if the software were a human using different, less efficient means.
Let's take pre-Elon Twitter for example: Twitter's API allowed automated programs to tweet things without simulating a browser, "clicking" on "new tweet", putting text in the text box and then "clicking" on "send". Instead they could directly send the text and identification info to a part of Twitter's API. This communication with the API happened through a protocol, most likely HTTP/HTTPS, because protocols have in-built ways to handle communication failures, encryption, etc.
Yes and no. It's not just the protocol but also the fact that Lemmy and bin both are fairly similar in function, making interoperability / connectivity much easier. kbin is probably even a little closer to Reddit in its native desktop layout than Lemmy, which most Lemmy apps also are following. It's one of the reasons why I went with kbin instead, but I also have a beehaw account which I primarily use for mobile testing, as kbins API isn't released yet, which means there's a distinct lack of proper mobile apps at the moment. Here's how my regular frontpage looks like at the moment, with a couple userscripts.
Thanks for a reminder that I should look into userscripts for kbin. — For now, I'm using the Stylus extension (in desktop Firefox & Chrome) to apply custom CSS. Nothing fancy yet, just simple overrides to remove some margins and padding to make the "compact" view more compact.