Let me start by stating that Elasticsearch is NOT a database, in the strict sense of the term, and should ideally not be used as such. However, nothing prevents you from doing it (and many people are doing it) and according to the good folks at Elastic, they won't ever strive to try and make ES a real database. The main goal of ES is to be a fast and reliable search and analytics engine, period.
If you can, you should always keep another primary source of truth from which you can easily (re-)build your ES indices anytime if something goes south.
In your case, option 1 seems to be the way to go since all you want to do is to allow users to search your products, so there's no point in synching the other tables in ES.
Option 2 sounds appealing, but only if you decide to go only with ES, which you really shouldn't if you want to rely on transactions (ES doesn't have transactional support). Another thing you need to know is that if you only have your data in ES and your index gets corrupted for some reason (during an upgrade, a bug in ES, a bug in your code, etc), your data is gone and your business will suffer.
So to answer your questions more precisely:
ES can be reliable as a primary source of truth provided you throw enough efforts and money into the game. However, you probably don't have millions of products and users (yet), so having a HA cluster with minimum three nodes to search a few thousands products with a few fields doesn't seem like a good spend.
When your products table changes, it is easy to reindex the table into ES (or even in real time) and if you have a few thousand products, it can go fast enough that you don't really have to worry about it. If the synch fails for some reason, you can run the process again without wasting too much time. With the zero-downtime alias technique, you can do it without impacting your users.
ES also provides snapshot/restore capabilities so that you can take a snapshot of PROD and install it in your TEST cluster with a single REST call.
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