Stars in multiple constellations Are there examples of single stars that are a part of multiple constellations? What about stars that are part of one Western constellation and one non-Western? 

Thanks in advance!
In traditional constellation shapes / outlines, yes. But the International Astronomical Union (IAU) standardised on a set of 88 constellations in 1922, and from 1924 to 1930 formalised the constellation boundaries, splitting the sky into separarate areas (that cover the complete sky) so there's no ambiguity now.

For example, before the constellations were standardised in 1930, the same star (on the boundary of Auriga and Taurus) was known both as Gamma Aurigae and Beta Tauri.

And the traditional constellations of Ophiuchus (The serpent bearer)  and Serpens (the snake) (Where Serpens ran across Ophiucus) was handled by splitting them into Ophiucus and Serpens Caput (snakes head) and Serpens Cauda (snakes tail). 

see http://www.ianridpath.com/boundaries.htm for more details.

Different cultures have different traditional constellations. If you have a look at the free Stellarium program (see http://stellarium.org/), that has a set of overlays showing constellations from a number of different cultures. (I don't remember if that's part of the standard installation, or an optional extra you can download).