Regarding Cassandra's age, you do have to consider that people in that setting grow up sooner than we do in the real world. I don't think the age difference is that big a deal.
What I said above. I find it hard to think a 30+ year old given to the Chantry as a warrior wouldn't know anything about Templars. They're just as ignorant as other characters. Which tells me they're fresh faced and young.
Chantry Bro/Sis works, but they wouldn't be Temps necessarily. That's what I ended up doing.
I just wanted to weigh in since I play a human warrior (SnS) who is in fact 30 at the start of DAI.
The ONLY thing the Trevelyan non-mage codex says is (emphasis added),
The Trevelyans are nobility from Ostwick, a city-state on the southern coast of the Free Marches. It is an old and distinguished family, in good standing among its peers, and with strong ties to the Chantry. Its youngest sons and daughters—those third- or fourth-born children with little chance of becoming heirs—often join the Chantry to become templars or clerics. As the youngest child, Lord/Lady [Player name] Trevelyan was expected to follow suit... until the disaster at the Conclave.
[Player name] was present at the Temple of Sacred Ashes as a representative of his/her family's interests, along with other distant relatives in the Chantry. He/She was the only survivor at the temple after the explosion. Rumors that the mysterious mark on his/her hand is a sign of the Maker's favor were spread by those who claim they saw the divine prophet, Andraste herself, lead Lord/Lady [Player name] out of the Fade.
It does NOT say that you are definitely part of the Chantry, or that a non-mage has already been sent to the templars. As far as I'm concerned, the player can headcanon that in any way they wish, just as you did. I have a headcanon to explain it that I'm satisfied with. This is one reason I like that the DAI origins are so vague, because you can have a more loose interpretation.
We also have the example of Sebastian, who appears to have had a misspent youth, sowed his wild oats, and so on, before he was given to the Chantry.
However, I will say that even a non-mage Trevelyan in these circumstances should know more about the templars since, presumably, they have had other family members who are templars. There is also a disconnect with some of the questions that you are able to ask Giselle. But we know why those questions are there, don't we? They're there for the new player who has no knowledge, or for roleplay purposes. You don't HAVE to take those questions if you want your character to be more familiar with the templars (or mages, or Dalish lore, or whatever else). I'd argue that being selective in the investigate options is also a part of roleplay.
You could also look at it in another way, which is that the PC has a broad, general knowledge of the templars, but not the more Order-specific things, like details about lyrium addiction and so on, which appears to be something that is not widely discussed outside of the Order.