No, the elements of the Dragon-Blooded are not so simply determined, though an unusual element is likely because your father married into the family, and you inherited his element.
Backgrounds: This isn't a complete list, but it is the basics, and how I'll implement them.
This isn't an Exalt in Creation. This is an Exalt who did something stupid during Calibration and got thrown into another world. Therefore, any background that isn't possible to have taken with her will be something she's managed to develop in the past few months with local resources. Backgrounds can be acquired in play, though some are more difficult than others.
Followers: Followers are people who work for you. In this case, it would be something along the lines of: Follower 1: An unmarried daughter of a local family who wanted to see the world has decided to tag along, probably helped by your social skills. This would give you a mortal servant, to do things that would be inconvenient to manage yourself. You could get this in play, but it would be less convenient and more difficult. You will have to provide for this person. More dots would give you more loyal and more competent servants, to an extent, but they are still mortal humans with the usual skills found in a farming village. You will have to provide room and board for them. You may have to pay them, depending on the rating.
At one dot, you will have a adventurous teenager. S/he will work for you, but will get annoyed if you keep telling them to do normal things, like handle your chores to save you time, because they want to be adventuring. They are also a mortal humans, so you might have to figure out something that won't get them killed. At two dots, they'll be personally loyal and you won't have to pay them, but you'll still have to provide room and board. At an additional dot, they'll be willing to do normal things and not require cool things to do.
Allies: This is like followers, but instead of a mortal, it'll be someone going to the same sect that you already know and are friends with. They'll like you, but they aren't personally loyal. This is a friend, not a servant. Each dot will give them more potential, basically, a more competent ally.
Artifact: This is a magic item of extreme rarity that she had on her when she got transported. Each dot makes it a more powerful artifact. Because she is a Dynast, it is probably a family weapon. This is powerful, but also specific and might raise questions. (Why do you have an extremely expensive magic item way beyond your supposed background?)
Familiar: This is an animal loyal to you. At one dot, it is a mundane animal, basically a pet. At three, it is a supernaturally intelligent pet (A small child) or a dangerous mundane animal, and you can store and draw power with it.
Cult: Cult is people who worship you. An exalt can draw literal power from the faith of mortals. This can only be taken at a single dot, and represents the worship of the town you have been living in. Note that the Immaculate Faith teaches that mortals shouldn't worship the Dragon-blooded, and that the Dragon-blooded shouldn't be doing this. Why exactly has your character done this? Did she decide that it didn't matter, because they are foreign peasants? Did the power go to her head? Did she do something so impressive that they started to worship her, and she was too awkward to make them stop?
Resources: Money. Plain and simple money. It represents, specifically, a source of income, which should be specified. Maybe this families farm is doing much better after you negotiated with the local spirits, and they are sending you a lot of the profits. Maybe you were taken into a well off family. Maybe the local nobility is sponsoring you, in return for future favors.
Connections: This represents contacts, mainly, people you know and can ask for information, introductions, and maybe a favor in a pinch. This might represent a spy network throughout local towns, being the center of gossip for a village, or something alongs those lines. It might represent a person who has favors from so many people that you can assume that someone will help them, as long as they are in a particular area.