I am not sure about the pronunciation rules of kanji in Japanese. I understand that there are several pronunciations for each kanji, and I am wondering how native speakers decide when to use which pronunciation. Example: In 日曜日, if I’m not wrong, the first 日 means SUN, pronounced as にち; the second 日 means DAY, pronounced as び. Is it the case in reality that when the same kanji expresses the same meaning in a word, it always has the same pronunciation? Referring back to the previous example, is it true that when 日 means Sun in a word, phrase or sentence, it always is pronounced にち？
As is the case with other languages, Japanese people parse and read sentences based on words rather than characters. English speakers can pronounce the "rough" part of rough, through and thorough differently without thinking, and that's because they remember the pronunciations based on words. Likewise, 日曜日 is a very easy word meaning Sunday, and Japanese people don't need to worry about the reading of each character every time they see this word. There are even many jukujikun like 大人（おとな）, 明日（あした）.
For some kanji, yes, a certain reading is strongly associated with a certain meaning. For example, the kanji 悪 typically means "bad" or "evil" when read as あく, but means "sick" or "hatred" when read as お. The kanji 楽 means "leisure" or "comfortable" when read as らく, and "music" when read as がく. (Most native speakers are unaware of this; again, they remember the pronunciations based on words.) However, in many other cases, the association of readings and meanings of a kanji can seem completely random, and you have to remember each word individually. Regarding 日, both にち and ひ can mean both "sun" and "day", but when it means "Japan", it's never read as ひ.