Will we be able to develop on the provided virtual machine or do we have to set up the same environment for development on our local machines?

Will we be able to develop on the provided virtual machine or do we have to set up the same environment for development on our local machines? If not, how can we deploy our progress on the production environment and test it?

The provided virtual machine on our server is only for production : we used it to measure your website. So you need to develop on your local machine and only push modification on the server.
There is no specific system of deployement (only SSH).

In fact, the setup is quite close to a real (professional) production environment :
You NEVER write, build and test your software on production servers, you write and build on your local computer, and test on dedicated environment. Then, when tested, you may deploy it on a production server.