A trademark sets your brand apart from competitors. If your competitors are other brands of mushrooms, then "Mushroom" is too broad. But if you're trying to distinguish yourself from other brands of packaging, it might work.
If it got litigated and I were the judge, I'd be concerned they were trying to abuse trademark to get patent-like protection. In the narrow packaging market, another mushroom packaging competitor would have trouble talking about its product without mentioning the word "mushroom" and drawing the ire of Mushroom™ lawyers.
Not certainly. A LARGE number of fungi grow just fine without manure. I think this is a common misconception since agaricus bisporus (portobello, bella, white, cremini, button) need it to grow well, and it is the most commonly human-grown fungus by a long shot.