You are correct that there is no push currently (we are exploring some ways to make it possible) and no admin panel (we are also exploring a lite admin panel), and no analytics (you should just use something like Mixpanel).

For cloud code, it's not true that parse-server doesn't support it - you can write cloud code directly in the node server.

For a full rundown on what's compatible, check out the migration guide: https://parse.com/docs/server/guide#migrating

The core functionality is there, and I highly recommend trying out the official Parse open source solution first, as it will be the easiest for most apps that want to migrate.