While Obi-Wan's desire to protect Coruscant is valid, Ahsoka wasn't at all prioritizing Mandalore first. Her hostility only came when she hears the Chancellor is involved, which means that the Jedi are going to pull all their resources to gain a political move much like what happened in "The Wrong Jedi". What Ahsoka was actually trying to say is: "While [Anakin and Obi-Wan] will be saving Palpatine, will there be any Jedi left to protect the people from the crossfire?"
Given that Shaak Ti was nearly close in uncovering Order 66, it would be logical of Palpatine to arrange her as his bodyguard and arrange his kidnapping so that Shaak Ti would be killed during the attempt. note She doesn't get killed during the battle, though since she dies at Anakin's hand.
Why does Almec call upon Diplomatic Immunity (or whatever variant one uses for "No I'm totally not harboring an enemy of the Republic now go away you're violating an ancient treaty I have no intention of honoring")? Because it'll make it easier for him to rally support against Bo-Katan and her Nite Owls, if he presents her as a vengeful renegade hell-bent on exacting revenge for the death of her sister. The fact that she's returning to Mandalore at the head of a massive Republic fleet and storming the capital city with an army doesn't help her case either.
Why aren't there any ARC-170 fighters or similar craft being sent ahead of the Republic-Mandalorian strike force? Because when Anakin and Obi-Wan left to fight in the Battle of Coruscant, they likely took every spaceworthy fighter they could, reasoning that Mandalore's preference for Proud Warrior Race Guy behavior would preclude them having starfighters of their own, which proves true. In addition, the fleet of warships that attacked Courscant was canonically incredibly massive, and they would need every vessel that could sling torpedoes into CIS hulls. It's also canon that one of the reasons that the ARC-170 fighter was used in the battle was because the Republic was throwing everything that was armed into orbit to stop the droids, even if they weren't great at dogfighting.
As awesome as it is to hear, the music that plays when Ahsoka leaps from gunship to gunship, fighting off various Airborne Mooks is the same theme from the opening battle of Revenge of the Sith...which must mean that said opening scene is occurring at that very moment. Anakin's fall to the Dark Side, the purge of the Jedi Order, the reorganization of the Republic into the Empire and Order 66 are just a few days away from happening.
In fact, if you play Revenge of the Sith from the beginning and this episode from the opening shot of the invasion side-by-side, Dooku and Maul will eventually show up at the same time.
Anakin not turning to Ahsoka for advice during the events of Revenge of the Sith makes a lot more sense with this episode's events in play. Besides the fact that they've told each other they'll talk when they get back, she's busy invading a planet and therefore has no time to listen to his problems...exactly as Palpatine intended.
We don't see any civilians during the battle, while they could just be hiding, keep in the mind that they've spent at least several months under the rule of a Sith Lord and his army of militant nutcases who are determined to return Mandalore to its warrior past. Considering how Darth Maul claimed that he's been planning to lure the Republic (and Kenobi) to Mandalore, he must've known that he would need a bigger army to stand a chance of winning an eventual showdown, and the fastest way to grow a military would be to literally drag people off the street, slap them in some armor, and give the minimum level of training. So all those Shadow Collective soldiers we see being shot at, blown up, or otherwise killed might not have all been there of their own free will.
