I think Minerva saved Lector because of her wierd abilites (how she teleported or w/e happy from nowhere into her arms) and her aim was just to provoke sting into taking action against that weakling of a Master (to me it was pretty obvious that he's all talk, I mean the difference in that guild were the 5 strongest members, popularity and strength- if the master was stronger from all of them how come they were a good for nothing guild before the timeskip?)
As to why, most of you already stated she has some plans and she's planning to take over. I guess with this I can really imagine her on the same level with Erza. Although Erza will beat the crap outta her, ofc.
Next, I'm also in favour of that girl being Lucy, I won't repeat what others said why though.
Third, I personally think Polyuska isn't Grandine, because well Grandine can easilly communicate through minds and who says other dragons can't? (reffering to Igneel) I mean, considering the fact that the dragons are from the start of the series the "big bosses" around it would be pretty wierd for them to not have a way to stay in tune.
As to why I think it's wrong to assume Igneel finds everything through Grandine is that when Grandine comes to him (in that world where they live in) he tells her to go away and asks her why she's here. So, no. I think the all-knowing thing would be more fitting if it has something to do with Natsu's scarf or it was imbued in the dragon slayer techniques. It's possible that the dragon that thought a person the techniques can see everything the person goes through, in my opinion.
Finally, what I'm most interested is WHAT will Jellal and CS in all do now that they know the situation better than others.