Are convolution and multiplexing synonymous?
Multiplexing is the name given to the process of stuffing/switching/packing multiple signals, channel, bits, etc into a single stream/medium/band, whereas the opposite act of separating each individual packed signal, bit etc, back is named as de-multiplexing. In multiplexing each signal (or bits) remains completely intact and have no kind of intersignal interaction other than errors and ditortions whatsoever.

Convolution, on the other hand, operates on two signals and produces a new third signal which is somewhat like the child of the two parents. It's properties are related to its parents by the mathematics of the convolution process. Usually a convolution will be used to produce the output signal of LTI systems where the input signal is convolved with the system impulse response. Rarely a convolution between two arbitrary signals also considered (especially in frequency domain, which is more of a theoretical guide rather than a computational one, circular DFT convolution being an exception). The opposite operation of convolution is named as deconvolution and seeks for finding the driving input from a given output under different constraints.