Can anybody anywhere in the world 🌍 create a website like lemmy and Mastodon with possibility of creating multiple instances and feed it into the fediverse so that it gets shared into both lemmy and?

You can post to Mastodon and tag Lemmy community and the Mastodon post will appear as a Lemmy post.

There are significant limitations to this approach such lack of graceful support for thumbnails, markdown (doesn't work on the Mastodon side) and URLs. I.e. it's only good fat basic text posts (or image only posts).

Now that WordPress has official ActivityPub support: yes, pretty much. Posting to both Mastodon and Lemmy will be a challenge, though, as Lemmy doesn't really offer following individual users.

Technically, any website can be an ActivityPub server, so you could "trick" Lemmy into thinking your website is a community while "tricking" Mastodon(-likes) into treating it like a normal feed. That's pretty messy, though.

Yes. This is how the internet was meant to be and how the Fediverse works. I just posted an Owncast lviestream to Lemmy and you could watch the livestream right in Lemmy. SOmeone can comment or like a Peertube video from Mastodon and it reflects on the Peertube video itself. It should all interconnect.

I'd recommend checking out piefed.social as well as what others recommended.

Or better yet, build your own if that's what you're thinking. :-D Always room in the fediverse for more projects imo!

You want a website and software that does Lemmy and Mastodon at the same time? That'd be kbin / mbin.

In part because of the kbin creator's real world struggles, it hasn't really taken off quite as well as Lemmy has, but its successor mbin is in use in a few places. I'm currently on fedia.io which is an mbin instance, for example.

If you mean the ability to post at both at the same time, on the same site, there's mbin.