There’s nothing special about Julia with any of this
how are the intellectual property rights of its package developers protected?
If you have intellectual property rights, it would be up to you to protect them. You’d have to identify people violating your IP rights and take legal action
For instance, if a developer creates a Julia package and uploads its code to GitHub as a public repository, how does he prevent others from plagiarizing
That would be scientific misconduct, and you should report it to the journal/university
his code to develop new packages, or extracting its principles for academic publications, or for commercial purposes?
These would be governed by the license you choose, although with open source, “develop new packages” is mostly what you want to encourage.
Can a Julia package be cited as a reference in academic papers? If so, how should it be cited? What would be the appropriate citation format?
If in doubt, contact the authors. If there is a paper associated with the package, cite that. Otherwise, follow the guidelines of the journal you’re publishing in. Generally, I go with <Name of Maintainer> and Contributors, <Name of Package>, <Github URL> (Year of last release)
If one develops a Julia package with some academic significance, should it be made public after the publication of the associated paper?
It should be made public before the publication of the paper. This is actually pretty important.