For the character"冒"，is the top part "日" or "曰"？
For the character"冒"，is the top part "日" or "曰"？


Neither.

冒 is comprised of simultaneously semantic and phonetic 冃 (mào, hat) and phonetic 目 (mù). The word that both 冃 and 冒 originally represented is now written as 帽.

Components are usually added on when the original character is too simple (and so can get confused with something else), or when the original character is overloaded with too many other uses (in this case, 冒 is used for things like 冒汗, 冒險, 冒認).


  In general, are both "日" and "曰" used as a radical at the top of some characters? How to distinguish them?


When you are asking about just a part of a character, not talking about dictionary header entries, then they are just charcter components (部件), not radicals (部首).

Anyway, have a look at

https://japanese.stackexchange.com/questions/3635/whats-the-deal-with-origin-of-the-character-曰/61301#61301

towards the bottom, where it is explained that you can’t tell 日 and 曰 apart in another character, unless you have an understanding of the character’s history, or at least the function of its components.