Think of federation like the Hawaii Islands. It's a group of types of social media, and they're kind of similar.

Each island has its own flavor and way of traveling to other islands though. Meaning, some have commercial airplanes and some don't,, so you have to travel with your own personal boat to certain islands. Same with federation, you have the twitter style of Mastodon where they can post on the reddit style of Lemmy, but lemmy can't really post on Mastodon.

Piefed is a reddit style and you can't really tell the difference to lemmy, other than Piefed seems to have a better user interface. I haven't personally tried Piefed, but the features they brag about seem great.

There are all kinds of other types of federation (or islands) that are similar to other social media types. There's youtube, tumbler, instagram types, etc. They may or may not be able to communicate with lemmy back and forth easily.

An instance is just a computer (or many computers) someone has set up to handle all of the traffic and data, that's it. That's why some instances don't get back to you, that instance owner may have had something personally come up, or they're not really working on the project anymore. Some may be owned by big corporations as well, we just don't know.

I hope this doesn't confuse you more, but feel free to ask any questions and I'll try my best to answer them quickly.