A room mode is a large peak in response, or a null, which is a deep, narrow depression. So I would charaterize your dips as troughs, not modes.
Bass traps primarily reduce low frequency decay times (i.e. the time it takes the signal to fade away). They also tend to minimimze any peaks and troughs as well, but not totally eliminate them. However, most traps are not effective down at 40 Hz. The ones that are are very large and/or numerous. IOW, they take up a lot of space in a room.
There isn't one really, at least not a strong one. There's more of a relation between phase and frequency response than SPL. Perhaps John can give a better informed comment, but IMO the phase graph is mostly a "FYI" thing. There is no inherently "wrong" phase reading, and about the only thing you can do to change it is to relocate the speakers, or change the physical dimensions of the room. You should mainly be concerned about frequency response, because that's something you can actually hear, and make some adjustments on if necessary.
Regards,
Wayne