tl;dr: Looms have no reference on screen, and are contraindicated by the presence of Time Lord children.
First, there is no canon.
Canon in Doctor Who is something the producers ignore and the fans fight over.
"Canon" implies that some authority with the power to make official declarations about the franchise laid out what did and what did not actually happen. No one in an official position in Doctor Who has ever done that. Both Moffat and RTD have gone on record saying that they don't think canon is possible for this franchise.
The generally accepted fan notion of "canon" (from here out "fan-canon") is, so far as I can tell, as follows:
If it happened on screen in an episode, then it actually happened. If things that happened contradict each other, they still both happened. If it didn't happen on screen in an episode, it might have happened (but doesn't have to have happened if you didn't like it) unless and until something on screen contradicts it, in which case it probably didn't happen but if you like it you can say it happened anyway.
Non-episode on-screen events like minisodes, Proms, and Red Nose events are usually considered fan-canon, but get evaluated on a case-by-case basis. Audio stories, novels, and comics are not considered proper fan-canon, but often become fan-canon later when they are used as inspiration by the show's writers and appear on screen that way.
Interviews and other non-published works have the least likelihood of making it into fan-canon or headcanon, including RTD's declaration that the woman in The End of Time is the Doctor's mother. Producers and writers have said a lot of really silly things which never made it to the screen, and we should feel at liberty to pick and choose which of their ramblings we pay attention to.
So no, looming is not canon. It's not really fan-canon either, but it's special.
Looming appeared in the novel Lungbarrow, never on screen. However, Lungbarrow is inspired by the multi-season arc known as the "Cartmel Masterplan" which would have appeared on screen if the show hadn't been cancelled. We don't know how closely Lungbarrow follows the Cartmel Masterplan in its specific details, but Looming is pretty essential to the plot's main conceit.
So the Looms acquired a special place in peoples' head-canon during the Dark Years when the show was cancelled and the only new sources of published Doctor Who stories were novels, audio stories, and comics. The Looms represent "what should have been" for the series, and are associated with the fandom's grief for the cancelled show.
Looms were never mentioned in Old Who, and recent New Who revelations --you've mentioned several of them-- imply that the Looms are not on anyone's mind in the modern production team. So they're an important part of fandom history and many people are attached to them, but even by the Doctor Who fandom's flimsy notion of canon the Looms probably aren't canonised.
Can we make them fit anyway? Yes, of course, but it's pure speculation.
Gallifreyans used Looms because they were cursed with sterility. If they managed to overcome that sterility (perhaps during the presumed tech boom of the Last Great Time War), then (even if Looms were still used by the higher classes or the more tradition-bound families) there would still be children on Gallifrey. Indeed, if it was the first generation of children in ten million years, then the destruction of Gallifrey would mean even more.
Problematically, we've also been shown a child who's supposed to be the Doctor. Loom-people are created as adults, so this means that screen-lore-wise the Doctor wasn't Loomed--at least, not as we understand Looming from the expanded lore. ...Unless the child-Doctor is actually the Other, whose childhood pre-dates Looming. But that's getting deep into Unlikely Speculation territory.
