1) historically, they existed in the time period echoed in most high fantasy.
Are you sure about that? Are you sure you aren't taking that date from the armor?
Let's remove the heavy armor, for a moment. That armor is, as others have noted, is 15th-16th century stuff: Renaissance era.
Robin Hood is set in the days of Richard Lionheart - that's the 1100s, aka 12th century. Not a fantasy, but a referent of relevant archetypes and tropes, yes?
Charlemagne (from whom we get the term "Paladin") had his nights in the 700s and 800s.
Saint George (from whom we get much of our dragon-slaying penchant) is often depicted in heavy armor. But, for cyin' out loud, he died in 303!
We get some of our other dragon-slaying tradition from Siegfried - oldest manuscript for him is 1200s, and there are people mentioned who are variously dated to the 6th century.
The oldest manuscript of Beowulf is from the 800s.
King Arthur (once you strip off the armor layered on by Romantic-era authors) is a figure best placed somewhere around the 6th century, give or take. Certainly the socio-political situation he's dealing with is not Renaissance Britain!
While Tolkien is not the end-all, be-all of high fantasy, but he's a pretty solid benchmark for the game, and sure as heck the War of the Ring isn't taking place in the equivalent of the Renaissance.
Dragonlance had Solamnic Knights in heavy armor, but for most other purposes, wasn't the War of the Lance set in something a lot more like Dark Ages?
You see the trend, here?
Now, there will certainly be fantasies solidly placed in something like the Renaissance. But it seems to me that most high fantasy is actually more like Middle Ages (in social structures, politics, and economics), with heavy armor tacked on - the armor isn't a telltale of the age, it is itself an anomaly.
You wonder why guns seem anomalous? That's because the situation depicted in most high fantasies really isn't from the era of the gun! Adding a gun isn't adjusting high fantasy to match its real-world era. It is adding another anomaly.