1. This is a complex topic, but basic ideas is that we clearly define the behavior of the API in conflict situations. Most writes are "set" operations, which is simply last-write-wins. Well-structured apps can use this for the vast majority of features. For cases where you need multiple clients to modify the same data, we provide a Transaction operation, which ensures the write happens atomically. See:
https://www.firebase.com/docs/transactions.html
2. The service is ready for production apps now, and we have many already (Twitch, Klout, TED, BitTorrent). We have a rigorous test suite, comprehensive, redundant monitoring, data replication, and backups in place. At this point the Beta label is largely there because we haven't built the infrastructure to handle payments yet. You can expect that label to come off in the next few months.
1. How does Firebase handle data conflicts? (e.g. I delete a to-do item on my iPad while offline, then edit it on my iPhone while online. What happens when the iPad comes back online?)
2. When do you plan to leave beta/can I use this for production apps yet?