Would Your Inquisitor Welcome Children Post-Trespasser?

What if they're in a homosexual relationship?
For my IQ? Yes Josie's family are probably itching for an heir anyway

I imagine my Inquisitor and Sera might adopt someone, likely at Sera's behest, partly (or strictly) because cookie recipes.

Answering for my 'canon' Inquisitor: oh hell no. She was in a relationship with Blackwall, who is dead, and there is no way she'd want to raise a kid alone, if she was willing to do it at all. Some of my other PCs might be interested in bearing and/or adopting kids, though.

I think that in general RPGs should never give a player-created character kids without input from the player. (I am still mad about the end of Rasaad's romance in the Baldur's Gate Enhanced Editions for that reason. I know there's a precedent with Viconia, but that doesn't make it better.) However, I'm all in favour of games giving the player the option to have their character become a parent, especially when the protagonist is going to vanish off screen and they don't have to account for it outside of epilogue text.

I'd imagine one or 2 of my quizzies that fell in love with Cullen would be open to the idea of having kids with him but it depends on the quzzy

I'm pretty sure it is optional. I've seen people decline the proposal on Youtube and Cullen was cool with it.

Borrowing Andraste_Reborn's phrase: speaking for my "canon" Inquisitor Lavellan, she is interested in having children but she does not want any at the moment because of the looming threat from Solas. She does not want to bring a child into a world that might end soon and where she wouldn't have much of a presence in her child's life because she's trying to help prevent the end of the world. Basically, she thinks it would be irresponsible to the child and to her duties.

That said, after the threat has been concluded and depending on how it ends? Yeah, I could definitely see Lavellan raising children, blood, adopted or both. I don't quite see her being inclined towards a romantic relationship, though. I think she's had enough of that for, at least, a decade or more. It's not completely unlikely but not in the cards at the moment.  

I strongly dislike children and I don't want them ruining my video games as well, so MAKER NO.

For the sake of my own sanity, I headcanon that "accidents" are impossible in Thedas. Or at least in my particular instance of Thedas.

They've got magical healers (so they won't drive abortifacient herbs to extinction, like the ancient Greeks did), and are unlikely to have cultural hangups about birth control and abortion.

The hangups real-world cultures have are a surprisingly modern invention. Hormonal BC was initially praised by religious groups as more "natural" than alternatives. Abortion used to be a standard, uncontroversial part of a midwife's job, even among very devout communities. IIRC, doctors made it into a big deal initially because they wanted a bigger slice of the business. Later, religious political groups latched onto it as a wedge issue, with the implied problem being that it encouraged sex outside of marriage.

It's not impossible that could also happen in Thedas, but their major religions don't feel as negatively about fornication (except for some jobs within the Chantry), so it seems less likely.

What about condoms?

That kid needed pushing down a flight of stairs or two.

I wholeheartedly agree.

Well, when syphilis was rampant, the alternative was a descent into madness followed by an agonizing death.