You can interact with the nodes, which are what provide access to the blockchain. There are some programming interfaces that make it pretty easy. I use those for my various scripts. As long as some nodes are operating the blockchain cannot easily be shut down. There some apps (such as Ecency) that remove the need to use the web to use Hive. We need this diversity to keep it running.

I know some witnesses have a witness PC at their own place so they have full control. From what I understand it doesn't have to be all that powerful, but it needs a fair bit of memory and storage. It would be interesting to know what the minimum spec would cost. I am out of touch with the latest hardware. I last built a regular PC some years ago.