I am new to Japanese and I've seen several questions similar to this one, but not exactly that one. If this has been asked before, I am very sorry.
In our class, we introduced weekdays and the Kanji for them. Until then, we only had the Kanji for couting (e.g., 一 and so on), for which I could manage to pronounce them correctly (e.g., while 四 is usually よん, 四時 is よじ, just because I know that 4 o'clock is not pronounced yonji).
However, for 日曜日, I cannot really comprehend how we get to にちようび. I understand that 日 has several readings, and ひ・び and にち are among them. All weekdays contain 曜日 - ようび - which means "day of week". Hence, as 日 is read as び here, I assume ひ・び to literally mean "day". As 日 can also mean sun, it makes sense that 日曜日 is Sunday, as it's composed of 日 - Sun and 曜日 - day of week.
However, the first occurrence of 日 is pronounced にち（にち曜日), and apparently, にち does not mean sun. For example, まいにち（毎日）is "every day", and here にち means day. This would imply that にちようび is "day day of week" which does not make sense to me. I cannot understand a) why we read the first 日 as にち and the second as び, if both mean day (I know one is the sino-Japanese reading and one the original Japanese reading, but I cannot make sense on how to derive this).
And b) next to not understanding why we read 日曜日 as にちようび, I also don't understand why it means "Sunday" and not "Day DayOfWeek" (obviously, that doesn't make sense), as にち (as well as ひ・び?) means day (as in まいにち) and ようび is the day of week.
I've read that beginners should just "accept" 日曜日 as Sunday, but I want to understand how to parse/read/understand Kanji. I think I still do not really understand how they work.
Thank you so much for your help. I hope I've made my question clear...