WordPress Multisite with different domains and themes

What you’re describing is a WordPress multi-site install. Everything you described will work.

The WordPress Codex has most of the information you’ll need to get started:
https://codex.wordpress.org/Create_A_Network

As of WordPress 4.5 domain mapping is native to WordPress and you don’t need a plugin.

https://wordpress.org/support/article/wordpress-multisite-domain-mapping

It’s a pretty straight forward setup but following the guide above and / or doing a bit of googling will definitely get you through it.

The most involved part will be adding the different domains, which some of that work will need to be done through hosting / registrars.

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