Initially, when Anna first met Hans, she became instantly infatuated with his good looks and charm. As the two became more acquainted with each other and their lonely pasts, the two soon shared a romantic duet which ended with Hans proposing to Anna, which she gladly accepted despite having known him for a day. While Anna was away, she proclaimed that Hans would be in charge during her and Elsa's absence. While it seemed during Anna's absence that he truly cared and loved her, when Anna returned to Arendelle to receive a true love's kiss from him in the hopes of healing Elsa's curse inflicted on her, Hans revealed he never loved her and how he only planned to marry her to become king of Arendelle and kill Elsa to ensure this.
He left Anna to die as he went to kill Elsa and any feelings Anna had for him disappeared. She managed to interfere with his plans and save Elsa by using her frozen body as a shield to block his killing blow and got her revenge on Hans by punching him off the ship they were on. It should be noted that due to her years of loneliness and desperation for love that Anna's "love" for Hans was nothing more than a small crush based on his outward appearance and her belief that she would not have another chance to find someone else while her feelings for Kristoff were genuine and based off of real love. Even Hans has stated how she was so desperate for love that she was willing to marry him. It is also apparent that there is no (longer any) affection between the two sides as Anna hates Hans for the monster he truly is and Hans never truly cared for Anna at all but was instead using her infatuation for him to get Arendelle's throne and was willing to let her die to further his own fiendish schemes.
When Anna refused to leave without her, Elsa created the giant snowmonster Marshmallow, and he threw Anna, Kristoff and Olaf out of her castle, telling them to go away. He threw Olaf, which angered Anna into saying "It is not nice to throw people." While getting ready to throw the snowball at Marshmallow, Kristoff stopped her, telling her to leave the snowman alone, but gave Kristoff the impression that she was calm. Anna threw the snowball at the giant snow monster. Angered by this, Marshmallow chased after them, though Anna was able to launch a pine tree into Marshmallow's face. While Anna and Kristoff were descending down the cliff, Marshmallow started to pull them back up and he shouted at them to not come back. Anna, out of fear, replied they wouldn't, and then cut the rope so that she and Kristoff could get away from the snow monster.
The Duke of Weselton
The Duke of Weselton was polite to Anna as with her sister and even danced with her (after Elsa told him her sister dances) and asked her if she know why the castle gates were shut but she said she did not know. When Elsa's powers were revealed, he was briefly hostile towards her asking if she has magic like her sister, but Anna and Hans reassure him she is ordinary. Anna and Hans argue with the Duke that Elsa was not a monster but the Duke refuses to believe them. When Anna says she will go to get Elsa the Duke quickly agrees showing that by this point he was not to concerned with Anna's safety. When Hans was giving out necessities to Arendelle's citizens The Duke showed that he did not trust Anna believing that she and Elsa were conspiring to doom them all. But in the end, the Duke showed that he had began to care for Anna a little as he showed grief when Hans lied to him and the other Dignitaries that Anna had been "killed" by Elsa, where the Duke was the first to say that there was no doubt that Elsa was a monster.
Duke of Weselton