The chick in the first one didn't know there were billions of daleks surrounding gallifrey at the time presumably ;p From the pre-show clip about Arcadia, it was a total sneak attack on gallifrey, which they thought was impregnable.
Was there any indication that the moment could kill all daleks everywhere ? I got the impression that it was just blowing up gallifrey and the surroundings, which happened to contain almost all the daleks at the time.
My understanding from the (admittedly possibly non-cannon) alternative media stories is that the Dalek push against Gallifrey was entirely because the war was becoming so time locked that the Daleks basically made an all in attack involving every Dalek everywhere and everywhen. Attacking the Time Lords on their home turf demanded nothing less. It was not really as lopsided as the special shows, because you have things that have been discussed before (Davros's ship going down at the Gates of Arcadia, ect) that point out the extent to which the Daleks were getting pounded, too. The high council also pretty much does not give a shit about the average Gallifrey citizen (numerous examples of this over the years), so once the Daleks breached the defenses of Arcadia, they most likely would have pulled their remaining military resources to the capitol and let the average derps get mowed down. There are also tons of people living primitive lives in the wastelands that surround the cities, themselves, that the Daleks would likely have spent some time killing, too.
As far as the Moment is concerned, if this was a weapon that even the Time Lords were not willing to use in the face of their defeat, then I would say that it likely had that capability. According to a lot of the backstory of the series, Rassilon was quite the asshole and cranked out numerous super weapons to cement his reign. Two of these are actually shown being used in the old series. The first is the Time Looper, which puts an entire world in an endless time loop trapping the enemy race before they can ever become a threat in and endlessly trapped from the point in their timeline that the Time Lords choose, which is their principle method for dealing with threats to Gallifrey. The second is the Demat gun, which erases the target from existence entirely, as if they never were, which was used by the Doctor on invading Sontarrans and a rogue Time Lord at one point in the old series. According to background material, Rassilons snuffatron gauntlet is essentially his personal Dmat gun. These were weapons the Time Lords were actually willing to use, so if the Moment is nastier than those, I would have to imagine that it would be pretty fucking powerful to the point of too dangerous to ever be in the hands of one person. Its also possible that some of these forbidden weapons were relics left by the Guardians of Time (sort of super entities that watch over the timestream), which is true of some of the Gallifrey tech, but I doubt they will ever clarify it to that extent.
Now, as for how the Daleks were ever a match for the time lords, there is probably too major things that caused it. First, the Time Lords violated their own non interference rules and tried sending the Doctor to go snuff them at the time of their creation. He failed in this task and it essentially made this a fixed point in time, preventing any other attempts at it. Second, knowing that Time Lords were trying to snuff them out, the Daleks systematically devised their own time travel technology, possibly from stolen Time Lord tech, ultimately leading to the direct conflict that would persist from the 5th Doctor era onward. Basically, the Time Lords more or less set things in motion by trying to make the first move and in doing so made it impossible to use their normal time cornhole weaponry on the Daleks.
