> How/where would content be stored?

Modern web browsers have a real database called IndexedDB. The users store the content. Most users, of course, would not store most content. Users that wanted to could run the app full-time on their local machine, where the database would be leveldb instead of IndexedDB. They would store much more data. Not all data would necessarily be saved forever.

> Also, how much would you expect each message to cost?

Payment channels reduce the cost of transactions to next to zero. An "upvote" does not actually go on the blockchain - only when channels are opened or closed to transactions go on the blockchain, incurring a transaction fee.