Why does observation collapse the wave function?
In the following answer I am going to refer to the unitary evolution of a quantum state vector (basically Schrodinger's Equation which provide the rate of change with respect to time of the quantum state or wave function) as $\mathbf{U}$. I am going to refer to the state vector reduction (collapse of the wave function) as $\mathbf{R}$. It is important to note that these two processes are separate and distinct. $\mathbf{U}$ is understood well and can be modelled accurately with the equations of QM, $\mathbf{R}$ is not well understood and it is some physicist's thoughts that QM will need to be modified to incorporate this state vector reduction process.
There is much to say about the $\mathbf{R}$ process, but I will address your question directly; basically "is it consciousness that reduces the state vector/collaspes the wave function?". Among those who take this explanation seriously as a description of the physical world, there are those who would argue that - as some alternative to trusting $\mathbf{U}$ at all scale and believing in a many-world type view point - that something of the nature of this $\mathbf{R}$ process occurs whenever the consciousness of an observer becomes involved. E. Wigner once sketched a theory of this kind in Nature in the 60s. The general idea was that unconscious matter or inanimate matter, would evolve according to $\mathbf{U}$, but as soon as a conscious entity becomes physically entangled with the state, then something new comes in and actually reduces the state (some $\mathbf{R}$ process).
The posit that it is consciousness that causes this collapse is very hard to debunk, due to the very nature of this type of argument. However, if you consider the following example, it should be clear that this picture is far from complete; and that this argument for consciousness causing the $\mathbf{R}$ process is not sufficient. Consider the weather, the detailed weather patterns that occur on any planet, being dependent of chaotic processes, which much be sensitive to numerous individual quantum events. if the $\mathbf{R}$ process does not actually take place in the absence of consciousness, then no particular weather pattern could ever establish itself out of the morass of quantum-superposed alternatives. Can we really believe that the weather on these planets remain in complex-number superpositions of innumerable distinct possibilities - just some total hazy mess quite different from actual weather - until some conscious being becomes aware of it and then at that point, and only that point the superposed weather becomes actual weather? I don't think so - do you?
Personally I think we can expect some amendment to QM if this process $\mathbf{R}$ is ever going to be sufficiently explained. One candidate model to explain this reduction process is the gravitationally induced state-vector (and its decedents). There are strong reasons for suspecting that the modification of quantum theory (QT) that will be needed, if some form of $\mathbf{R}$ is to be made into a real physical process, must involve the effect of gravity in a serious way. Some of these reasons have to do with the fact that the very framework of standard QT fit uncomfortably with the curved-space-time that GR demands. Yet most physicists seem reluctant to accept that it maybe QT that needs adjustment to facilitate a successful union with GR. Roger Penrose describe a new model (based on other candidates) in his book The Shadows of the Mind (not an easy read!) that uses a quantum gravity model to explain the elusive quantum process $\mathbf{R}$ - this is well worth a read if you want a better understanding of this mysterious process and it implication on human consciousness.
I hope this helps.
An electron, indeed any particle, is neither a particle nor a wave. Describing the electron as a particle is a mathematical model that works well in some circumstances while describing it as a wave is a different mathematical model that works well in other circumstances. When you choose to do some calculation of the electron's behaviour that treats it either as a particle or as a wave, you're not saying the electron is a particle or is a wave: you're just choosing the mathematical model that makes it easiest to do the calculation.
The next question is OK what is an electron then? At the moment our best description is that the electron is an excitation of a quantum field. Using quantum field theory allows us to calculate the behaviour of electrons whether they happen to be involved in particle-like or wave-like interactions. This doesn't mean that the electron is a quantum field, and we'll almost certainly replace quantum field theory by some even more complicated e.g. some future development of string theory.
The collapse of the wavefunction is a separate issue, and one that has generated much debtae over the years. I think the general consensus is that the collapse of the wavefunction is a manifestation of a more general process called decoherence.
In different interpretations of quantum mechanics the definition of "measurement" is different. But I think it would be enough if I give just five of which you can choose yourself.
In Copenhagen/von Neuman interpretations the collapse of the wave function is triggered by the observer. This person has the special property which no other object in universe is capable of. In Copenhagen interpretation the collapse can be triggered by any system which is connected to the observer, including the measurement apparatus and external medium (if the observer is not isolated from it). All things can be arbitrarily divided into the observed system and the measuring system by so-called "Heisenberg cut" with the only requirement the measuring system include the observer.
The von Neuman interpretation is the edge case of Copenhagen interpretation where the Heisenberg cut is placed as close to the observer as possible. As such even the parts of his brain still be be considered the part of the observed system. In von Neuman interpretation the collapse of the wave function happens when the observer feels any qualia(feeling) depended on the measured value.
In Bohm interpretation the collapse of the wave function happens when the observer introduces into the measured system some perturbation, which is inevitable when performing the measurement. The difference between the measurement and any other interaction is in that the perturbation introduced by measurement is unknown beforehand. This is because initial conditions of a system containing the observer are unknown. In other words, the observer always contains information which is unknown and cannot be determined by any means due to self-reference problem. Thomas Breuer called this phenomenon "subjective decoherence". The philosophers believe that this unpredictability of the system containing the observer for himself, defines the free will.
In Relational interpretation the collapse happens when the interaction affects the ultimate measurement performed by ultimate observer on the universal wave function at infinite future. As such, for the collapse to happen the result of interaction should somehow affect the external medium, the stars, etc, either now or in the future, rather than being recohered and lost.
In Many-worlds interpretation the wavefunction collapse never happens. Instead what the observer perceives as the collapse is just the event of entanglement of the observer with the observed system.