Let me try to answer:
- Yes, it’s a structural VAR. See section 4.3 of Del Negro/Schorfheide (2004).
- My understanding is that you are estimating the DSGE model parameters by combining a prior on the DSGE model with combined DSGE model and VAR estimated on actual data. That way you get a posterior on the model parameters. Again, see Del Negro/Schorfheide (2004). If you now change the weight of the DSGE model fit relative to the VAR fit on the data, of course the posterior will change.