Commenting on theory 1, I too could believe that Shallan has the royal locks, and the reader is intentionally lead to believe lightweaving changes her hair color. In fact, I think Shallan herself assumes it's a lightweaving related ability and only Formless really understands.
Going off of the paraphrased Warbreaker annotations on Coppermind, "Like Returned, wearers of the Royal Locks can also change other aspects of the physical appearance. With practice, wearers are able to change their age, height, and body shape." So, if this theory already assumes Shallan has royal locks, we can assume that even her aging and basic appearance may be a manifestation.
Assuming that, I believe it's possible that Shallan is not related to the other Davar's and replaced the original Shallan sometime during the original's childhood. I believe Formless is her true identity and that she's been working with the Ghostbloods since the beginning. Formless has taken care to manipulate her age and appearance to grow and mature as the original Shallan would have, but is likely much older. If she has access to royal locks then she would have access to this ability.
Related to this theory, I don't know if bonding Pattern was part of the Ghostblood's plans or not, but I think it's possible. Shallan also references heightened sense for color, even saying Veil only sees plain, dim ones. It's not impossible that Formless has access to breath and heightening. Pairing Formless with Pattern would be a viable way to give her access to stormlight as a replacement for breath (although I don't fully understand if a bond is needed for someone with breath to make use of stormlight, or to what degree it improves its potency).
Other related questions to the theory that I don't have reason to assume one way or the other would be "Is Formless a Returned?," "Why is Formless working with the Ghostbloods?", "Why was Shallan an important role to usurp?", ect.
In my head cannon, I really want Formless's dark unforgivable secret to be related to either stealing the breath or the lives of thousands of people. That would give her a vested interest in the Ghostblood's mission to get stormlight off of Roshar and replace more controversial investiture systems like breath.
In my SUPER fanfiction head cannon, Formless is Shashara, Vasher didn't kill her like he thought. Creating Night blood and the tax his power takes, let alone the lives he's taken, may be what's haunting her and why she's trying to find a better investiture system for her research. She may be using the Ghostbloods since they have a synergistic goal.
