Posts, comments, replies, and likes database schema
Your question would be easier to read, if you included the references for your foreign keys.

I'm guessing that user (foreign key) refers to field id in users table (not displayed), and similarly with post.

With those two, as well as with the other foreign keys, I would attach _id to the name, so that it's clear they are ids and not names.

You don't specify primary keys. Did you already designate id in each table to be the primary key, and has auto-increment? If not, make sure you do. 

Other than that, I think it's pretty good.