itch.io

It depends, send some photos with your museum so we can help you.

Don't play it, you need to talk with her and she will proceed with the missions.

It's in the museum.
Idk if you can do it instantly but you will find it in the museum aka gallery.

It's not dying but just think how big game developers take years to make a good game and they are working full time, this team is working when they have free time so it's obvious it would take more then it would take a full time team to make a new update.
The new update comes in about 3/4 days so just be patient.
If you would like the game to release faster you can subscribe to their patreon so they would be able to work more on the game instead of working like once a week maybe.

In 2 weeks from the early access release, that means in about 3 or 4 days :D