They don't "communicate" faster than light, the wave function itself is non-local and collapses non-locally.
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Sure, but anything that tried to explain the observations would be a dark matter theory, and if that theory involved particles, it'd be a particle theory.
Dark matter isn't a theory, nor is it particles, it's just a body of observations that's poorly named. In that sense, dark matter definitely exists, we just don't know in what shape or form.