The reason she didn't kill Armin on the battlefield to me is no different with Jean's case, as he was also there together with Armin and Reiner. The difference would be Jean's assault towards Annie that led to his injuries.
Beside that, I think that she harbors feeling for Eren. She is the one who taught Eren how to fight, to the point that Mikasa getting jealous of their interaction and physical contacts as we can see in the new flashback. What could her motive be other than that?
Annie did not hesitate in her attempts to abduct Eren, very well knowing that, in the hands of her superiors, Eren would have awaited the same fate that Ymir had suffered... Obviously no strong feelings shook her judgment. Annie respects Eren and his focus, but nothing more.
And Mikasa’s jealousy reflects her misperception and nothing else: after all she was jealous of Eren even to Historia. Does this mean that Eren and Historia in some hot secret romance (or at least an emerging romance)? No. Simple like this.
The question with her feelings for Armin is quite different.
If she had been influenced by guilt and/or pity when 17th episode happens, she would have killed Armin anyway (back then or later at Stohess). Because guilt and pity did not stop her and the others from getting rid of Marco. In fact, after Marco's suffering, she could have made Armin’s death very quick one. Now that would be out of pity... Or she even shouldn't dirty her hands with his blood, and just call pure titans, as she had done with the right flank. But she saw him and she didn't.
Annie didn't even have to go to all these troubles to establish his personality - I'm sure that in 17th episode, the reason she even show interest in blond because two others (more skillful) officers wasted their lives try protect him - tipping her that this blond is someone important (they all didn't hidding their faces back then, but they did moving a lot). Enough to die for (remember Ness' specific order to keep her away from Armin. Instead to, I dunno, going ahead and warn commander and others - 30% rookies will die anyway, so why he?.. Meaning that Armin really important for Erwin and it was known to Ness and anyone who count, but I get distracted ). But during all of this, she had received enough glimpses of his face (and do not forget the important part about Eren's behavior or lack of it) to know that he was anyone but Eren. But for some reason she wanted to get close look instead. And then she spared him, twice more.
Moreover, it was because of his intervention that she spared Jean: was she distracted by Armin's words? Didn’t want to kill his fellow cadet-and-kind-of-friend in front of him (now that he is obviously fully conscious again)? No idea, but before that she did not hesitate to kill everyone who dared to stand in the way. And this is fact.