Yes, distributive adjectives can be used with both singular and plural nouns..
“Each” refers to individual items being considered separately, while “every” refers to all items in a group or set.
No, “either” is specifically used for two choices.
No, “neither” is specifically used for two items that do not meet a particular condition.
Yes, there are other distributive adjectives, such as “per,” “apiece,” and “respectively,” but they are less commonly used.