Frequency Encoding Gradient
INCORRECT. This is the action of a RF excitation pulse (a magnetic field oscillating at the Larmor frequency).
INCORRECT. The MRI signal has been oscillating away as soon as the RF excitation pulse was applied. "Reading out" a signal is simply a case of recording the voltage in an appropriately placed receiver coil. With or without the frequency encoding gradient, a signal can be recorded. However, the frequency encoding gradient is applied during the recording of the MRI signal. Why is a this? What does this accomplish?
The frequency encoding magnetic field gradient effects a change in the Larmor frequency in one direction (left-right in this case).
CORRECT. The frequency encoding gradient is a static gradient field, just like the slice selection magnetic field gradient. It does the same thing; it causes range of Larmor frequencies to exist in the direction in which it is applied (according to the Larmor equation).
By causing this range of frequencies to exist, we can use the Fourier transform to separate them out after we measure an MRI signal (which is a mix of all signals from a slice).