If I have a wave on a string, can any wavefront be defined for such a wave? And also is it possible to have circularly polarized string waves?
If I have a wave on a string, can any wavefront be defined for such a wave?
In general, a wavefront is defined as a connected set of points in a wave that are all at the same phase at a given time (usually at the phase corresponding to the maximum displacement.) For a wave traveling in 1-D, the points at which the string is at the same phase are disconnected from each other; so in some sense, each wavefront consists of a single point.
This actually makes sense if you think about it. For a wave traveling in 3-D, the wavefronts are two-dimensional surfaces; for a wave traveling in 2-D, the wavefronts are one-dimensional curves; and so for a wave traveling in 1-D, the wavefronts are zero-dimensional points.
And also is it possible to have circularly polarized string waves?
Sure thing. You have two independent transverse polarizations; just set up a wave where these two polarizations are 90° out of phase with each other. The result would be a wave that looks like a helix propagating down the string. The animation from Wikipedia below was created with electric fields in a circularly polarized light wave in mind; but the vectors in the animation could equally well represent the displacement of each point of the string from its equilibrium position.