You can meet with minister Belisse during the Of Somewhat Fallen Fortune side quest, i.e. one of the quests connected with Josephine (to learn more, see the appropriate page). During this quest, you can go to the party in Val Royeaux. Here, you get the opportunity to meet Minister Bellise and you will be able to try and seduce her, to your ends (restoring the aristocratic status to the Du Paraquette family).
During some of the conversations with Vivienne, you should note dialogue options marked with the heart symbol. You can choose them and strive for the enchantress' attention, but you need to know that you cannot enter a relationship with her, nor start a fleeting romance.
You will be seeing Harding, at the beginning, only after you reach a location for the first time. It is a good idea to be nice to her, each time, thanks to which you get dialogue options marked with heart, in the dialogue box. You can decide on a longer meeting with Harding some time after you reach Skyhold. You can find her near the tavern. During the conversation, you can state that you only wanted an innocent flirt, or tell her that you care for a more serious relationship. It should be noted that this mini-romance, does not stand in the way of any of the romances described above, because you can break up with her at any moment, without negative consequences (Harding is still going to welcome you in every location that you visit).