I have been trying to ask about this over on the Physics Stack Exchange, but they aren't really interested in questions that are this speculative. Does anyone here have any ideas about what quantum particles "are"?
The way you asked the questions seems to imply that you subscribe to a substance metaphysics. But it seems to me that the way modern physics has progressed, it presents us with a manifestly process-based metaphysics. Thus, as a general rule of thumb, if you're asking really fundamental questions like "what is a particle" physicists will not be able to tell what it is as well as they will be able to tell you what it does given a certain situation. So if you want a real answer to your question, you need to give an operationally-defined question. (For example, what happens to electrons when they are fired straight at a metal under the influence of a strong E field? What if they were fired at a crystal? Hint: very different things will happen.). Nevertheless, since physicists in general do not pay attention to philosophical matters, they find themselves asking your very question, and although their answers are fascinating, they could also be described as abstract nonsense.
Nobody knows. We model them as wave-like perturbations of the appropriate zero-point field for the characteristics we are interested in. But a zero-point field is just a label to hang the basic mathematics on, we have no idea whether that makes any ontological sense either. And as I have been discovering on the Physics SE, there are many fundamental questions for which this quantum field theory (QFT) has no direct model and just fudges its way past.
The standard approach is to simply ignore the ontological issues and just use the math, fudges and all, to predict experimental results.
Any attempt at a real physical concept is known as an interpretation of the theory. Provided the interpretation is logically consistent with the maths, it cannot be falsified. There are a great many such interpretations, as I am sure you have discovered. The Copenhagen interpretation states that there is no such underlying reality of relevance to scientific enquiry, and because all those attempts cannot be falsified they are of interest only to metaphysicians.
Actually, it's worse than that. Historically, the ontological reality of the things which appear in the equations (such as the quantum fields), temporal causality, and the exclusion of faster-than-light or nonlocal influences, have all been taken for granted. However we have discovered through the famous entanglement phenomenon that these three - causality, localism and realism - cannot all be true. Physicists are left scratching their heads over which one or more of them is false and what they might want to test for in the lab. Since this has philosophical implications at least as profound as its scientific ones, Einstein's observation that scientists make bad philosophers is rather coming home to roost at the moment.
Again, part of that problem is that the quantum field equations are set on the pre-existing stage of Einstein's spacetime. Some physicists suggest that actually, space and/or time may be emergent properties of dynamic quantum systems. In such case, the quantum equations must be recast accordingly, but we have no idea what to aim for. So we don't even know what playing field we are on, never mind what game is being played on it. Despite this, the rulebook that we have compiled for the game is probably humankind's greatest intellectual achievement to date.
Quantum entities completely break our intuition when we try to understand them (reason for which Feynman stated in a lecture that "if you think you understand quantum mechanics, you don't understand quantum mechanics"). It is quite difficult to define what is a quantum entity. Like a sphere is something that is not the rest of the space delimited by it, an entity is something that is not the rest of the universe, but, where, when, what, how are the limits of quantum entities? For now, there's not an agreement on that. It is perhaps acceptable to say that a quantum entity is basically a mathematical model, an idea, a concept, which, when used to predict some specific behaviors, works extremely well.
Try not to approach quantum entities as things of our daily experience. They are not. So, you might have departed with the wrong foot when asked "what is __ like": there are few similarities. Here, a couple of hints that might help you starting (hope being right, I'm far from being an expert):
Statics: existence in the quantum universe is radically different.
Nature, at a quantum scale, is different from what the nature we are used to perceive, the macroscopic scale. Macroscopic entities have shapes, occupy space, remain static in time, don't move, don't disappear, can be broken in parts, etc.
But small entities, at the quantum mechanics scale "are" just different. I've quoted the word "are", because they exist in a different way. Part of their existence is determined by the observer (you, when you "observe" a quantum entity), and part of it is determined by rules, not perceptions. So, in simple words, the existence of a quantum entity, for you, depends on what you do and on certain rules. That is quite different to a beach ball, which will remain in the sand if there's no wind, if you don't look, or if it does not lose air pressure. If a beach ball would behave like a quantum entity, it would not be something that we could touch, but moreover something we feel in the air (they don't really exist in space); it would not lie on the beach, but probably lie on the beach all the time (according to a wavefunction); it would be like a breeze, and at the same time, a storm; not one or the other but both at the same time (superposition); once you've hit it --something that could happen or not--, it might just appear on the other side of the beach without traversing all the space over it (quantum leap); it might exist simultaneously in multiple spaces or behave depending on another ball of the same beach (entanglement), etc. It might even change past actions when you kick it (see Wheeler's experiment)!
Notice that I've quoted "observe", and said "what you do", and not "what you perceive". That is because we cannot directly look at quantum entities, because they are of the size of the same photons we get into our eyes. This leads to the next hint:
Dynamics: "to observe"/"to measure" a quantum entity, in books, means really "to interact with".
Since we can't directly observe or measure quantum entities --not even with a microscope--, we need to interact with them. So, observing, in quantum mechanics, is not a passive process, but an active one.
We do this, essentially by "launching" other "particles" against a quantum entity, which is like throwing rocks against a rock to know its color (luckily, we've had extremely intelligent scientists that found ways to answer equivalent answers in equivalent conditions). I've quoted "particles", because a quantum entity is not really a particle, but an excitation on something called a field, which is more or less like what is sound to air. And I've quoted "launching", because we can't really "launch" something that is not a particle, but we know how to produce some phenomenon that allows an interaction between two quantum entities, which is something quite complex. Following our analogy, it is not like listening a sound from a punctual spot in space, but producing an additional sound and assess the effect in the surrounding context.
Notions of interaction (action, reaction, causality, sequence, etc.) of our daily experience do not have direct equivalences in QM.
The analogy I generally use is that particles are like knots or purls in a fabric. If you think of an energy field as a smooth continuum (a three-dimensional equivalent of a two-dimensional sheet of fabric), and then imagine that somehow the fabric got snagged or tangled into a lump than, well... that lump seems like something different than the surrounding smooth field. But that's mainly a trick of topology.
I mean, what is the essence of a knot before it gets tied? Measurement 'ties the knot', so to speak, and before that all we have is the potential of a knot.