Like Filecoin? Or is everyone connecting to your one server…?

I'm going to say probably not, but depends on your use case.

Putting data on a blockchain is closer to a p2p system. You release it out in the wild and then have little direct control on it. For me, the primary driver of self hosting is taking ownership and control of my data and systems, where here you still primarily rely on other people's systems.

The systems you have Interacting with that data ? Maybe.

It's a bit ambiguous question:

A) If you are hosting the blockchain "at home", then by definition you contribute to the consensus of the network and you are just hosting the blockchain. Self hosting becomes irrelevant as your node becomes part of the never ending non reputation party.

B) If you are are enabling people to host data ON the chain itself: Well, good luck on future technical interviews if you put that on your resume :P

Self hosting is a state of mind maaaaaannnnn

I think I've you can set up your own local $ETH chain for the purposes of testing out and developing smart contacts. Otherwise, a chain with a single source of concensus (your server) kind of defeats the purpose of using a block chain to begin with

No.