If a particle has multiple quantum states (for position) in superposition, can it be at multiple places? When a particle like an electron is at x position, it is at a quantum state for that position. If it has more of these states, can it be at more positions?
 A: Until we measure it, and therefore fix it's position (for the time of measurement only), the idea of it having "a position or positions" is not really meaningful in quantum mechanics. 
A: Short answer is that when you do a measurement to find a particles position you will always measure it to be at one position $x$ with a measurement uncertainty of $\Delta x$.
Every wave function $\Psi(x)$ will already give you a multitude of possible valid $x$ positions with different probabilities to occur. (note: $\delta(x)$ is not a valid wave function as it is not square-integrable)So you do dot need the superposition for the basis of your question. 
When you do your measurement to determine the current position of the particle, the previous state $\lvert \Psi \rangle$ breaks down to (i.e. will be projected to) a state in a basis which is given by your measurement $\lvert\Phi\rangle= \sum_{i} \phi_i \lvert\Phi\rangle $.
The wiki page about the Measurement in quantum mechanics is a good follow up to read.
A: A particle can be in quantum superposition, which can place it in multiple quantum states simultaneously.  However, if the particle is "observed", that is if information is extracted from it, the quantum states will decohere, and the particle then will occupy only the state in which it is "observed".
Researchers at the University of Bonn designed a clever experiment which may have succeeded in pulling a single Caesium atom to two places at once.  The had to use indirect measurements to avoid quantum decoherence.
A: It is only at one place at any given time which we find only by detection. It certainly is not at more than one positions at a time because that has never been detected experimentally.
