The graphic in your screenshot isn't a Park Transform but rather a Clarke Transform. It's in the stationary reference frame since there is no angle dependency. The use of "dq" labels in the model might be a bit misleading in that regard.
In your test model it looks like you haven't quite sorted out what reference frame you want to implement your model. The reference frame selection is arbitrary, but needs to be consistent. Stationary and rotor reference frames (based on rotor mechanical position & number of pole pairs) are convenient to implement, but a textbook would give you a more complete description (e.g. Analysis of Electric Machinery and Drive Systems by Krause has a good discussion).
The state-source errors could be due to a variety of reasons. One subtle reason might be in the misapplicaiton of "Allow state space inlining" parameter for the controlled sources. If the source is not a static, constant linear combination of circuit measurements (e.g. use of cos/sin in rotating reference frame transformation) then you should not enable that option. More specifically, you should not use a transformer-based implementation of a reference frame transformation (as used in the PLECS library component) if you're not using the stationary reference frame.