How to customize the Discourse app using docker container?

You might get away with the docker version if you can use existing plugins or theme components to perform the required customisations (there’s a lot of existing stuff you can use without getting too dirty - take a look through the plugin and theme categories).

Otherwise you need to look at developing your own plugin as pfaffman suggests.

You don’t even need to install dev locally btw - I use a cloud server.

More of my tips on getting started with plugin dev here: