Hi Farhan,
Open edX is built on Python and Django. Other things in use include MySQL, MongoDb, Elasticsearch, RabbitMQ. I don't know what you are planning to develop, so I'm not sure which of these you will need to deal with.
Developers work in a virtualized environment call devstack, which is currently based on Vagrant and Virtualbox. There is active work to create a Docker-based development environment.
It's impossible to say how long it will take to learn the stack. I don't know what you are trying to build, or what you already know, or how fast you learn :)
--Ned.