Unfortunately using static equations for calculating switching losses do not take into account lots of aspects (see here: https://forum.plexim.com/8369/mosfet-losses-calculation-in-thermal-wizard-via-formula). We therefore can't really bound the loss calculation like we can with table data (where we would always recommend having a zero loss datapoint at 0V/0A by the way). Perhaps you can contact the manufacturer and inquire if they have any switching loss data they can provide to you for this device.
By the way, I do wonder if some of the error messages are not because of this, but are referring to losses that are calculated while operating in a range that doesn't seem a good match for the device. For example, in your model, the FETs see ~2A currents but are rated for 120A. Therefore, the data that you can see in the datasheet is typically for much higher current ranges than 2A so you are not really able to get good resolution of conduction loss data in your operating range. This might be something for you to consider, and likely also is related to why the switching losses are getting negative calculations.
But to answer your second question, we typically see that the channel resistance is similar for positive and negative current operation, so you could mirror the Q1 conduction loss (gate-on) data to the Q3 (negative current/negative voltage) quadrant. Do ensure you also change the losses at 0A to be 0V, though.
Finally, even if you can add some resolution to the data yourself to suppress the error messages, I do think you should understand the limitations of the switching loss equations and therefore should not rely on the results to give a high degree of accuracy.
I hope this helps, but let me know if you have further questions.