Kate's first command center was notable for having a tree growing up through the floor and roof. Her new yacht base in this series is called the Sequoia, which is, of course, a type of tree.
Speaking of bases: where was that first base of Kate's? In a skyscraper. Where is Bruce's Batcave? Deep underground. So where is Kate's new op center, now that she's more associated with Bruce and has similar accoutrements on her global missions, yet still remains, y'know, the Kate we know and love? Where is the midpoint, in other words, between high in the air and far below the earth? Sea level, on a ship.
Issue #1 establishes that Bette Kane is attending West Point, and therefore isn't operating as either Flamebird or Hawkfire. In #2, Kate uses a flamethrower built into one of her gloves, when previously her gloves had housed tasers. It's plausible that Kate incorporated some of Bette's old gear into her own since they weren't being used.
At first, the arrival of the warlords so soon after the lighting of the beacon at the Desert Rose seems to not only be a Deus ex Machina, but a violation of time, considering how fast they get there. But remember that Kate shlepped Rafael at least half a mile from the docks to the inn, while it was not yet fully dark out. It's not unreasonable that at least one of the warlords could've spotted her, put two-and-two together, and told the others what was up and where to go.
The detonators on all the explosives are deactivated with an EMP that Kate stole from Julia's personal stock... very similar to how Kate stole military equipment during her earliest days as a vigilante.
All of Kate's fights with Knife in the first arc involve Kate keeping her distance as best she can (batarangs, flamethrower gloves, etc) rather than getting up close and brawling. This is because Knife was armed with bladed weapons (obviously) and Kate has a history of getting stabbed. The techniques she was using would minimize the chances of that happening.
Issue #11 takes place in Cairo, and features a flashback of the Kane twins going trick-or-treating... dressed as mummies.
With the introduction of Coryana and its fox population, both Kate and Bruce's pasts before they became vigilantes now involve the animal in some way; in Bruce's case, it was the movie he watched with his parents shortly before they were murdered, The Mark of Zorro ("zorro" being Spanish for "fox").
The severity of Kate's mental and emotional strain, especially after her fear toxin exposure, is given some context in issue #12. There, an untrained and out-of-practice Kate is able to do just about as well as (and maybe even a bit better than) modern-day, impaired Kate against Tahani, who was already an assassin in the flashback.
