A) Duplicate the way as an administrative border. Administrative boundaries should [almost] never reuse other linear features such as waterways, roads and railways. However, they may (and should) reuse other administrative boundaries. If you plan to work within the existing Wels relation, split the existing 11 boundary ways as needed.
Note that suburb boundaries should be verifiable somehow: if pretty much everyone agrees what are the exact boundaries of e.g. Lichtenegg, feel free to add them. However, if it’s just a vaguely defined area, better leave it as a place=suburbnode as it is now.
B) If you duplicate the border as in a), then you do not have to split the railway. However, in general, we’re pretty liberal in splitting ways whenever a need occurs – such as maxspeed or even smoothness change, or when the segment joins or leaves a route relation.
Specifically for these situations, unless you have a single-track, the border won’t follow one track in the pair of double tracks anyway. Exception would be eg it has been doubled to one side, and the border has been exactly defined as the previously single-track. However, then you have to consider whether it has ever been realigned, adjusted along platforms, etc. So in any case, please duplicate it, and move it to the middle.