The person inside the Female Titan was Annie Leonhart, a soldier from the 104th Training Corps and a warrior from Marley, who used her unique Titan ability to fight and gather intel on Paradis Island, eventually crystallizing herself to avoid capture. She was a highly skilled martial artist, trained from birth to be a warrior, and her Titan form was a key part of the Paradis Island Operation, as noted in this Attack on Titan Wiki article.
Around the year 843, Annie Leonhart was chosen to inherit the power of the Female Titan.
Annie was praised as impeccable for her fighting abilities and was later chosen as one of seven promising candidates to inherit the power of the Titans. She was later granted the power of the Female Titan in accordance with her stellar combat skills.
Why did Annie try to kidnap Eren? Secondly since he was the attack Titan there was a high chance he also had the founding Titan in him. Excluding this the reason she kidnapped him was to bring him back to Marley to have a warrior from there eat eren.
Annie just created the crystal to avoid being captured and so that the scouts couldn't do anything to her.
It's not made clear if Annie and Armin ever end up together or not. The idea that Armin inherited his feelings from Bertholdt is probably not true though.
Instead of killing him outright, the Female Titan -- Annie -- decides to lift his hood and confirm whether or not he was Eren, as that was her objective. Even after the encounter, the Female Titan decides to not kill Armin.
Clash of the Titans arc
Due to the fog, they can barely see the body of a very tall Titan slowly moving toward them. After closer inspection, and as the Titan gradually comes closer, they both realize it is Dina, the exact same Titan that devoured Eren's mother five years prior.
The nine Titan powers were the Founding Titan, the Armored Titan, the Attack Titan, the Beast Titan, the Cart Titan, the Colossus Titan, the Female Titan, the Jaw Titan and the War Hammer Titan.
After the end of the manga, we learnt that Eren killed 80% of humanity and the 20% of it mostly lived in Paradise Island. What was believed to be a lie at the start, turned out to be a reality in the end.
Annie is genuinely selfish, due to having been abandoned at birth and being used as a tool by everyone she has ever known, even by her adoptive father who wanted a better life for himself through her. She has no interest in protecting strangers due to being unattached to most of humanity to an absurdly high degree.
Levi Ackerman (リヴァイ・アッカーマン Rivai Akkāman?), often formally referred to as Captain Levi (リヴァイ兵長 Rivai Heichō?), is the squad captain (兵士長 Heishichō?, lit. "leader of the soldiers") of the Special Operations Squad within the Survey Corps and is widely known as humanity's strongest soldier.
Annie Leonhart - Annie was an Eldian baby abandoned at birth and Leonhart adopted her. His goal was to solely train her into becoming a Warrior of Marley so that he could have a wealthy life while Annie looked to her adoptive father as a source of strength.
Hoping he will lead her to the real king of the Walls, Annie decides to follow him. When Kenny discovers and confronts her about it, Annie attempts to deceive him by telling him that she is his long-lost daughter. Unsuccessful in fooling him, Annie attacks Kenny and flees into the sewers.
As mentioned above, the Ackermans are immune to the power of the Titans -- their memories can't be erased by the power of the Founding Titan. The reason for it is that their bloodline has been modified, as they are no longer considered as Eldians who can turn into, and/or affected by the power of the Titans.
Eren used his power to direct Dina specifically to his parents' house at Shiganshina, so that she could eat his own mother Carla and drive the events of the story, basically manipulating his younger self.
The second was when Eren convinced Ymir that she had a will of her own, freeing her from the royal family's control, and she lent her power to Eren instead of Zeke.
The Cart Titan is in no way a weak link, but it can be considered the weakest of the Nine. Held by Pieck Finger for the run of the show, the Cart isn't built for direct combat or known for its overpowering strength.
Armin asks Annie's help to smuggle Eren out of the Capital, and she agrees. When they come to the tunnels Eren will travel through, she refuses to enter for fear of being trapped. It is revealed that Annie is the Female Titan, confirming Armin's suspicions. She transforms and begins to attack them.
The reason why Annie was so cold coming out of the crystal was because she knew the rumbling had started and concluded that her father was probably already dead. She lost the one thing she was living for so of course she was depressed.
We blame Annie for eliminating Levi's squad in the line of duty, and we glorify Floch even though he conspired for the same reason: to eliminate the same squad. In the end… the result is the same: they both participated in the killing of Levi's squad…
Eren's true love, widely considered by fans and supported by the creator, is Mikasa Ackerman, though their relationship is portrayed as tragic and complex, evolving from a sibling-like bond to deep, albeit complicated, romantic love that he struggles to acknowledge due to his grand, world-altering plans. He confesses his feelings in the end, but it's within a tragic context, acknowledging he couldn't bear seeing her with anyone else and seeing a future where they lived happily in an alternate reality.
I think what makes her didn't burst out crying is because she witnessed Eren killed people mercilessly too. She's still in shock. Not to mention that before she beheaded him. She was already crying from the last scene of memory in the path that Eren sent to her.