3 different sites with different domain on one WordPress

I’ve read the most of the post here but I’m still not sure what will be the best for me so I’m opening new Topic for my case.
What I would like to do:

1. 1 WordPress (with 3 categories cat1, cat2, cat3) installed on one hosting
2. 3 domain names pointing to this hosting (web1.com, web2.com, web3.com)
3. web1.com displays the post from cat1, web2.com – form cat2 and web3.com – from cat3 (no cross domain article visibility e.g. no access for some article from cat1 using web2)
4. Optional: 3 different templates for each site

Many thanks for the help