Okay, my turn.
Let's start with the English Longbow. They were quite nice, true. But here's the thing: they also took a LOT of time to learn how to use. While the Black Prince was able to field a respectable number of them during the Hundred Years' War, the numbers of such archers were limited. This was in part due to training time (it took YEARS to teach someone how to shoot one of those effectively) and bowmaking time requirements. Honestly, if these constraints hadn't been there, the face of Europe would look a lot different. At one point, wood for longbows was so scarce that the English Crown required ships coming into English ports to pay four planks for bowstaves as part of their port fee!
But compare that to the crossbow: technically a little more annoying to make, but still NOT as time consuming as crafting an English Longbow. Quarrels could be shorter, thus easier to make, and easier to procure materials. Slower to shoot, slower to load, and while you CAN volley-fire a crossbow, it isn't easy. But the thing is, you could feasibly field units of crossbow-armed troops more easily simply because they didn't require as intensive a training regimen. The wise commander would field both, as each had their own limitations.

Innocent II banned the use of crossbows "against other Christians" in 1139 at the Second Lateran Council.
Now, Zweihanders and the Romans. No, they did not exist side-by-side. But did you ever hear of a sword called the Dacian Falx?
https://en.wikipedia.org/wiki/Falx There were two versions. A one-handed, and a two-handed! They were an odd, sickle-like blade that looked kind of like a reverse scimitar with the edge on the INSIDE of the curve! Because they curved down and forwards, Dacian footsoldiers could bring them in a downward arc and pierce a Roman soldier OVER the edge of his shield! Well, sometimes. They weren't the end-all be-all though, because Dacia DID get conquered and added to the Empire.
NO, not all greatswords are Zweihanders!!! Most greatswords have a single quillion or guard with a long handle below (like a Claymore or Great Scimitar). A Zweihander has a specific handle-style with a secondary quillion/guard and grip that allows for a wider range of stances and combat styles. While used in warfare, a Zweihander is really a DUELLING sword! There was a rapier-like version in India called the Mel Puttah Bemoh:
https://de.wikipedia.org/wiki/Mel_Puttah_Bemoh
Likewise, a Flamberge? TECHNICALLY that is a style of blade design, NOT a kind of sword. The one linked in the earlier picture is a Flamberge-style Zweihander meant for warfare. The term is often synonymous with that particular type of sword. The serpentine profile allowed one to break pike and halberd shafts more easily. But longswords, daggers, shortswords, even rapiers were made in the Flamberge-style at one point or another.