We are using Robo 3t tool to interact with Mongodb. We could see the
user has read access on 2 databases but when the user is connected to
MongoInstance that databases are not visible to the users.
May be you have Robo 3t tool related issues (Such as certificate etc.), without log files can't exactly tell to that. But I would like to say that other than Robo 3t tool, you can use MongoDB GUIs Tools such as MongoDB Compass.
MongoDB Compass, MongoDB’s own GUI tool, supports the latest MongoDB versions and is available on Linux, Mac, or Windows. Introduced in MongoDB 3.2, Compass was developed to provide all the power of the mongo shell through an easy GUI tool. They always keep the free community version good enough to use MongoDB effectively, and you can expect them to improve this tool to continue enhancing its usability.
User has same permissions in other environments can able to see the
databases.
Yes
For further your ref here