Is there an objective, external reality according to quantum physics? In quantum physics, a particle can be in a superposition of two states until it is measured. In other words, the aforementioned particle doesn't have a definite state until it is "looked at" (measured). Since certain properties (i.e., an electron's position) of a particle aren't well defined until they are  measured, does this mean that quantum objects don't possess these properties, unless they are looked at? Do quantum objects even exist without an observer? Since macroscopic things are made of quantum particles, does the moon stop existing when no one is looking at it, since its particles don't have a definite position, momentum, etc.? Do the answers to these questions depend on the interpretation of quantum physics being used? 
I guess my main question is this: Is there an external, objective reality that exists even when it is not being measured?
 A: A superposition is a perfectly valid state in quantum mechanics. It simply doesn't have a correspondence in classical physics, which is the result of quantum mechanics (and not the other way around!). 

"In other words, the aforementioned particle doesn't have a definite state until it is "looked at" (measured)."

Yes, the particle (or better "the quantum system") does have a definite state: it's the superposition of two or more eigenstates. 

"Since certain properties (i.e., an electron's position) of a particle aren't well defined until they are measured"

They are perfectly well defined at all times. It's the act of a STRONG measurement which reduces the state to a pure state. There are weak measurements which do not. After the measurement the state is equally well defined, it's just not the same state as the system had before the measurement. 
All of this is perfectly "objective", it's just very counterintuitive to those who can't accept that the world is not classical. The world was NEVER classical, we merely have been looking at the world using the wrong description until we discovered the right one approx. 80 and some years ago. 

"Do quantum objects even exist without an observer?"

No more and no less than a falling tree makes a sound when nobody listens. That's an incorrectly posed question even in classical physics. 
A: The question you ask is a tough one and everyone has his own opinion about the answer (look at the comments of your question). In particular, one has to adopt a more or less clear philosophical position about what science ought to tell us in order to reply.
That being said, the decoherence programme tries to address some of the questions you wonder about. In particular, classicality is supposed to emerge via a "measurement by the environment" that projects a quantum system that ought to behave classically (like the Schrodinger's cat) onto a (quasi-orthonormal) pointer basis that so happens to correspond to the classical observables we are used to (e.g. a phase space projector or the dead or alive states for the cat).
In this process of einselection, it is often thought that there is not really an objective way of determining the actual pointer states.
Now, quite recently Zurek et al. have proposed a solution to the idea of objective pointer states (that has been quite acknowledged in the literature) which they have called quantum Darwinism.
My contribution would not be complete if I didn't give you a reference claiming that there is problem with the decoherence programme and in particular with the idea of quantum Darwinism. More about it here.
A: 
In quantum physics, a particle can be in a superposition of two states
  until it is measured. In other words, the aforementioned particle
  doesn't have a definite state until it is "looked at" (measured).

A superposition state is a state. So a particle in such a state does have a state before being measured.

Since certain properties (i.e., an electron's position) of a particle
  aren't well defined until they are measured, does this mean that
  quantum objects don't possess these properties, unless they are looked
  at?

No. It means that the particle doesn't have a single position. Rather there are multiple instances of it at different positions. Those instances can interact with one another in interference experiments, which is why you can't understand what it is doing by considering it as having only a single position. See
http://arxiv.org/abs/quant-ph/0104033

Do quantum objects even exist without an observer? Since macroscopic
  things are made of quantum particles, does the moon stop existing when
  no one is looking at it, since its particles don't have a definite
  position, momentum, etc.?

For a large non-isolated system like the moon, interactions with other systems prevent it from undergoing interference on a macroscopic scale. It does exist in multiple versions but you can't see the other versions, see
http://arxiv.org/abs/quant-ph/9612037

Do the answers to these questions depend on the interpretation of
  quantum physics being used?

Different "interpretations" of quantum mechanics make different claims about what is happening in reality. So they ought to be treated as different physical theories, not interpretations. Quantum mechanics without the collapse postulate implies the Everett interpretation:
http://www.daviddeutsch.org.uk/many-minds-interpretations-of-quantum-mechanics/
Other interpretations may have different implications about how the world works but they are usually ambiguous about what exists and some are apparently inconsistent or otherwise unviable.

I guess my main question is this: Is there an external, objective
  reality that exists even when it is not being measured?

Yes.
