I'm still reading through all the responses here as this topic fascinates me.
but my 2 cents so far:
mythal has a history of correcting, punishing, and making peace with other elven "gods". It makes a lot of sense that mythal, having used up her current body, would seek a new one which would also put her in a position to change the dread wolf in some way
I feel his feelings of regret are about giving coriphaeus the orb, and her regret is that she will have to change him and occupy the body
as mentioned mythal can't or won't take an unwilling host, so I think the dread wolf let her
I think solas was only dishonest in what he omits from truth. Telling mortals that he is a super powerful (or supernatural) ancient being would not be believed by many and other would not treat him the way he wants to be treated. Mythal takes this same course of action in the first two games, never revealing her true nature.
we have too much missing to tell the complete story, we need to know who killed mythal in her temple centuries ago, if it wasn't the dread wolf, and what was flemeths tragedy that caused her to call on mythal in the first place? Why would the dread wolf trust a darkspawn magistar with an object of great power?
your guesses are as good as mine on these questions. Hopefully we'll have some answers in the next game or in future DLC