Dragonkillers can fire skyward; the ones you use during the Steps of Faith launch into the sky before coming down on Vishap. Timing is essential in its use, but this is true of any weapon (particularly ranged weapons). Their exact range remains unknown; due to the heavy projectile it is not likely to be particularly great, but it is incredibly destructive. Their use during the Bismarck fight is... suspect at best, given the speed at which we were flying would make aiming a nightmare despite Bismarck's great size (they should be pointed at least a few degrees more towards Bismarck's face so after they launch the wind doesn't make you miss).

Despite Garlean machina's physical sturdiness, it is just as vulnerable to magicks as anything else. The Gilded Magitek Armor explicitly notes that even the thickest magitek armor isn't enough to deal with magicks, leading to the development of the gilded plating which is now standard issue. Even this can only dampen the effects of magicks, not nullify them outright. Thus, the counter to Garlean warmachina is clearly magicks.

The Ironworks' stated goal is "freedom through technology," not "superiority through technology" (or Allagan ingenuity). Cid's main goal with the Ironworks seems to be the production of consumer goods to improve Eorzean quality of life, not developing weapons for them to use; this makes sense, given his involvement with the Meteor Project and subsequent desire to atone for it. The Alliance has yet to use Ironworks-developed machina in combat against the Empire - the only known instance of magitek being used against the Empire was when we used a hijacked magitek armor to tear up the Praetorium near the end of Operation Archon, and that armor was made by the Empire (albeit modified by the Ironworks).

The Empire isn't incompetent; they just had a lot of issues and a bad commander in Stormblood. Despite everything, we were able to liberate Doma; this, combined with shinobi sowing dissent in the Imperial provinces, left the other legions unable to aid Zenos in Gyr Abania for fear of another civil war. Zenos himself is largely to blame for the Empire's loss - he could have won at Rhalgr's Reach but left due to boredom, then kept ordering retreats and surrenders to set up a big battle on the streets of Ala Mhigo that he ultimately lost. Note that despite appearances this still took tremendous effort - it took the combined might of all Othard to liberate Doma, and several battles were fought across Gyr Abania (Rhalgr's Reach, Castellum Velodyna, Specula Imperatoris, Castrum Abania, and finally Ala Mhigo), all of which took a heavy toll on the Alliance and Garlean forces alike. (We aren't shown most of this outside Specula Imperatoris, but it is there.)

... it's not a matter of the Empire being portrayed as incompetent or weak. It's a complex situation that shows the Imperial army has weaknesses like any military, all of which had to be exploited to win.

Side note: the Manacutters are not equipped with any sort of weapons. There is no reason they could not be, though.