Yes it allows searching for individual pages. Everyone can publish and index whatever files they want. However, they won’t appear under a domain name without being added by the domain name owner. Domain name are just for humans to read though, they are not required by ipfs and admarus. Nothing prevents you from cloning a website, modifying it, and publishing it under another domain or without a domain. Content published on IPFS is immutable and lives as long as someone has it. That means many revisions of a website can exist at the same time. Domain name are practical because they are made to always point to the latest revision.
No one can dictate what can be indexed. However, ranking takes popularity into account, so that spam and unwanted content doesn’t rank high