Hardware: I personally own/operate my own instance, so I own the hardware. In case of just signing up for random instances, they own/operate the hardware or rent the hardware. This does bring up a lot of possibilities, so if you are concerned about such things consider running one for yourself/friends.

Software: The software is open source under the AGPL license, so it's free to use. It is copyright the original author(s) or organization that wrote it, who control which license is used.

Protocol: The protocol specification is ActivityPub which is separate of fediverse projects and a W3C specification. This means it's as safe as HTTP or other common web protocols in terms of ownership.

As for censorship, each instance can choose to block other instances they deem are inappropriate. So the system relies on each community making decisions about what is acceptable and isn't acceptable. There will be servers that have more fringe content, and these will likely have the least number of federated instances due to other users not wanting to participate in this content.

Ideally, the users of each instance will agree with the policies that instance has. If not, they can move to another instance that more closely aligns with their preferences. It's also important to respect the policies of other instances, as they are choosing to allow instances to communicate with their user base. If they see an instance as a threat to their instance, it's only natural to take action. Where this line is drawn is based on the instance admin and by extension the instance users. This will lead to a less connected network as a whole, but allows groups to exist without fear of being removed for their personal preferences. This is of course ignoring legal requirements, which will be a concern for most instance operators.

As for politics, large politically active groups will most likely have many instances that align with their politics. Once things get political, they can get murky fairly quick. Any instance admin could push their politics onto the instance, it's up to the users to decide if that is ok or not. The only way this would lead to censorship/control is in the case of centralization, where a small group of entities (or single entity) run the largest instances. This is the reason the fediverse is pushing back against Meta trying to join the fediverse in my opinion. It's up to the user base to strive for a decentralized system, and all the tools to do so are public and free (as in speech, it does have an economic cost). It's easier to just "join an instance", but with convenience comes a cost.