My brilliant Swedish-speaking cousin responded to my email about the word poppy in Swedish:
"English and Swedish have common roots, so as you go back in time, Swedish and English words often look more and more alike. From what I have read about Vall on Gotland, the name probably just comes from a wall. Today, the Swedish word for wall is "mur," but the modern first definition for "vall" in the big Norstedts dictionary is embankment or rampart, so that makes sense. The modern word can also mean a pasture or grazing area.
Nothing ever translates exactly, of course. "Mos" is most often used for mashed potatoes ("potatismos"). Grandpa used to call Grandma's mashed potatoes and rutabagas "rotmos." (Rutabaga is "kålrot" in Sweden, but the British call them "swedes!")
For poppy, "vallmo" is the singular, and "vallmor" is the plural. The only way that an "s" would turn up at the end of the word would be in a possessive form (poppy's), so I don't -think- that mashes and pastures have anything to do with it. :-) "
Thanks cousin! I also found an amazing Swedish linen here - apparently it came from my grandma's house. It's covered in grease from years ago, but I hope I can bring it back to life.