[1] Foods in this song:
• 白玉 (shiratama): Small rice cakes, chewy in texture. It's similar to mochi, but the shiratama flour is made differently and gives a different texture. Shiratama dango may be shaped with a dip in the middle, like the shape of a red blood cell.
• 雲丹 (uni): Sea urchin roe. Sea urchins are round spiky animals that live in the ocean; the soft orange roe inside is edible. Note that the sea urchin itself is also called "uni", but the kanji spelling 雲丹 only refers to the food.
• 栗 (kuri): Japanese chestnut (Castanea crenata). It's a round nut with a spiky tip.
• 柿 (kaki): A variety of persimmon (Diospyros kaki).
• 梨 (nashi): A variety of pear from East Asia (Pyrus pyrifolia). 梨 may also be a pear, in general.
• たけのこご飯 (takenoko gohan): Steamed rice with bamboo shoots. Takenoko is used in many Japanese dishes and is in season during spring.
• おにぎり (onigiri): Rice ball 🍙.
• 木の実 (ki no mi): Fruits, berries and nuts that grow on trees.

"Uniguri" isn't a food; it's the name of that hedgehog that appears in Zutomayo's music videos.

[2] バッテン: A cross mark indicating a wrong answer ❌.
[3] 匹 (hiki) is a counter word for small animals and bugs. １匹 (ippiki) is one of that, but doesn't specify what exactly (could be anything, really).
[4] くれる (-kureru) implies something is done to the benefit of the speaker. This line is meant to read something like "time grants us neglect".