Our data set could have been handled fine with a relational database, honestly. However this was a rare case where over-engineering a problem and using the latest technology saved time.
- In 2011, it worked great on small data that fit in RAM, but once the data became bigger than RAM, queries would take unexpectedly large numbers of seconds. How much data do you put into Neo4j?
- I admired the friendly little web server until I realized that it was a massive security hole: anyone who could access it could run arbitrary code on the server, it ran over plain HTTP, and if you put it behind an HTTPS proxy, it stopped working. I hope this isn't still the case. Does it have reasonable access control and HTTPS now? Could you use the Web interface in production?
Every database benefits from having the _hot_ dataset in memory, so that's the same with Neo4j.
2011 was many years ago, since then the memory management has been completely rewritten. You very probably wouldn't use the Neo4j Browser in production as it is meant to be a developer tool. Usually, you would build an app that uses the drivers to connect to the db.
On (2), yes, the little UI now requires a username/password, and it supports HTTPS. HTTP remains available, defaulting to localhost access.