Or the 西 (xi1) in 东西 (dong1xi0) is pronounced with no tone?
No. It does not always apply.
xi0 might be another way of writing the neutral tone. I haven't seen it before.
For 东西, dong1xi1 (east and west) and dong1xi(thing) have different meanings.
To make sure whether a word ends with a neutral tone, without hearing how natives are using it, you'll have to look it up in a dictionary.