Hi Stg, welcome to the forums!
For iron, it is a common resource you can find in underground caverns. It should show up as a bright green dot on the map, and you can harvest it with fire touch, death touch, miasma whip, leafy whip, ice burst, ice cross, and i forget what else. You should be able to easily build up a stockpile after a few rooms.
When it comes to cherries, there are cherry trees you need to knock down in the same way, in the locations listed in the encyclopedia.
The same should go for anything like rubies, citrine, opal, jade, etc. Those ones will require finding the equivalent of a stash room underground, and are mine-able the same way as iron is.
Anachronism missions can be pretty difficult if you haven't played the game a bunch. You need to kill the enemies that don't belong to the area you are in. For example, if you are in an ice age area, skelebots are native to it, but fire espers or rhinos aren't. You would need to kill the fire espers/rhinos, without hitting the skelebots, as they reflect the damage back onto you.
Battlegrounds can be pretty tough, especially on the harder difficulty settings. I haven't run into the flare problem, but then, I rarely use them.
As for the bug report, it looks like it's listed as being fixed in the patch notes for the next upcoming beta patch.