My issue with this definition is how vague it is.

This is somewhat intentional. One should note that Libertarianism is not perfectly monolithic in its ideology -- in that it does not outline a regimented doctrine which must be adhered to for one to have the privilege of calling themself a libertarian. Instead, I would argue that it outlines a set of shared values being that one recognizes the importance of the state, but also possesses the goal to minimize it to the extent that is realistically attainable, and also that one possesses the desire to equally maximize the rights and freedoms of themself, as well as their fellow citizenry. You will find no exact agreement between libertarians on many precise social issues. What you will instead find is a set of common shared ideals with which they base their opinions.

what of liberalism

Liberalism, I would say, is where libertarianism inherits its desire for freedom. It outlines the philosophy that an individual should fundamentally posses a set of inalienable rights, e.g. right to life, freedom of speech, freedom of expression, freedom of association, equality before the law, consent of the governed, right to the private ownership of property, freedom of assembly, freedom of religion, freedom of the press, etc. This list is not meant to be exhaustive, but to instead give an outline to how I define liberalism.

what of minarchy

Minarchy, loosely speaking, is the desire to have a small state. Fundamentally, libertarianism will have the common denominator of a "Nightwatchmen State" in that the state should provide, at the very least, national protection through the military, and the enforcement of personal, and property rights through a police force and the judicial system.

The reason I think that is vague: what size is small enough?

I would argue that the minimization of the state is not necessarily a destination, but, instead, it is an aspiration. While you could say that "small enough" could be a pure Nightwatchmen State, I am very hesitant to do so, as it would be to assert that this is the ultimate, and perfect form of a minimal state, which I feel would be an arrogant statement to make.

And then which rights are necessary?

Answering this with precision, and confidence carries the same sort of issues as that of answering "how small of a state is enough"? The world is unfortunately not perfect enough to be able to create such exact, and precise rules. We instead must state guidelines, frameworks, and principles from which we base our opinions, and legislation -- we set our baseline, and determine on a case-by-case basis how laws fit in. One should be granted the rights to guarantee them maximal amount of freedom as can be realistically given so long as it does not infringe on the rights, and freedoms of others.

Some view the right to religion important, while others view the right to not have to deal with religion to be core, like in France recently not allowing hijabs in school.

The right to freedom of religion is not the assertion that one must practice a religion, but freely have the choice between them. It is the right to choose to practice a religion. I'm not well acquainted with the laws, and politics of France, but to ban one's religious wear is to infringe on their free practice of their religion.

Is the right to hate speech required?

I would encourage you to define that. I challenge you to come up with a definition that is not based in personal opinion. One should not have the right to not be offended.

Is the right to be noisy to my neighbor required?

These sorts of specific cases are usually left up to municipal bylaw, and tort law. A libertarian argument could be that no one should infringe on one's private enjoyment their life without their consent. If one incurred damages for such non-consensual infringements, they should be properly compensated.

Who even decides and enforces that?

Tort law is typically enforced by civil courts.