It's a sample size of over 150k across several studies.
Yes, but only 5.5% of those were meat avoiders 
This is the problem with media reporting of these studies. From the original paper:
"...study designs and a lack of rigor precluded inferences of causal relations. Our study does not support meat avoidance as a strategy to benefit psychological health."
"There were numerous issues that reduced the confidence in the published results. As detailed in our discussion, these issues included cross-sectional design, non-representative sampling, biased recruitment, the use of subjective (i.e., self-reported) dietary and psychological data, the failure to account for social desirability and observer-expectancy effects (e.g., reactivity), the failure to collect data on actual dietary intake, and statistical, interpretive, and communication errors such as the failure to correct for multiple comparisons, recognize regression to the mean, and the inappropriate use of causal language."
"Across all studies, there was no evidence to support a causal relation between the consumption or avoidance of meat and any psychological outcomes."