If I want to say only 日本 in a sentence then each character is pronounced in its onyomi version isn't it? If this is an exception and one (or all) of the characters is not pronounced in onyomi version then ok i'll remember the exception, but 日 isn't pronounced "ni" anyway. So how can I understand this situation?
There are no strict rules for how a word written in kanji translates to reading. There are rule of thumbs, but they do not give a strict indication. At best, they will give you a 40% chance to correctly guess a word's reading from its kanji. Which isn't trivial, but far from reliable.
Most of the stuff you've learned about onyomi or kunyomi is basically useless in practice, as words that actually follow those rules in a predictable way are actually in the minority. If you try to look at words that "don't follow the rules", or where the rules are ambiguous, as exceptions, you'll find that most of the Japanese language is made of exceptions.
Words like 今日, 昨日, 相応しい, or 大人しい, are great examples for having no clear relation between the kanji and reading. Even when a single kanji is used, you have examples like 全う, 全て, and 全く, all having completely different readings.
Even when a kanji has the same reading in multiple words, it can still have multiple options. For instance, in 男性, 可能性, 性質, 事件性, and 個性, 性 would be read as "sei". While in 本性, 性分, 相性, and 性根, 性 would be read as "shou". So even when it seems to "follow the rules", you're still getting a 50:50 guess on the reading.
日本 is actually closer to the latter case. 本 is quite often read as "hon" (while occasionally also being "moto"). 日 is most often "hi", "jitsu", or "nichi". The latter lends itself to both the reading "nippon", as in "nichi" with "chi" shortened to a small "tsu", followed by "hon" with "ho" upgraded to "po", similar to in 一本. "nihon" can be seen as farther shortening "nichi", or as doing something that is between "nichi" and "hi".
But really, if you're hoping to read any given word, you should learn the reading of the whole word, not try to divide it into kanji. After learning enough words, you will sometimes be able to spot kanji which are read the same in multiple words, and be able to use that to guess the reading of new words. But even then, it's anywhere between a 50:50 to 1 in 5 guess, and if you don't know the word, you'll have to look up its correct reading anyway. Kanji reading will serve, at best, as a hint or mnemonic.
There are three readings for 日本: にほん, にっぽん, and やまと. The last reading is non-standard as far as general use. The first two are still used often, but にほん is by far the de rigueur reading currently.
Possibly you are reading something old, where 日本 is written as につぽん. While today, a repeating consonant is written with a small tsu (っ), in the past it was often written with a regular-sized tsu (つ), and some elderly people still write it this way. What looks to you like Nitsuhon is actually Nippon.
日 has several readings, but the reading of に in にほん is a special case and shouldn't be applied outside of this circumstance.
(First, 日本 is pronounced like nippon or nihon, but not nitsuhon.)
Unfortunately, there are tons of irregularities and exceptions regarding the readings of words, and you have to master them individually, word by word. Pronunciations change over time, but spellings tend not to change. In the case of Japanese, there are even kanji words that completely ignore the original pronunciation of each kanji (known as jukujikun). For example 一日 is read ついたち.
- 日曜日，the different meanings and pronunciations of 日
- Where does the な in 大人 (otona) come from?
- Why is 一日 'tsuitachi'?
Uncommon words tend to exhibit less exceptions, so you don't need to suffer forever. English is one of the worst European languages in terms of spelling-phonetic consistency, so if you can speak English, you can master Japanese :)
日本 pronunciation is based on the on-yomi of each kanji.
You can "understand the situation" of
日本 being nowadays read "nihon" or "nippon" through its history :
- it is thought to have evolved from the go-on reading "nichihon" (ニチホン) to "nippon" (ニッポン) through phonetic change (called gemination or 促音便)
- and then from "nippon" to "nihon" for pronunciation softening.
Nowadays both "nippon" and "nihon" readings have been retained and are commonly used.
Incidentally, the kan-on reading of 日本,
ジツホン (jitsuhon), is thought to be at the origin of its translations in a bunch of foreign languages (Marco Polo's "Cipangu", "Jipang", "Japan", etc).
About your question and initial thought process:
I think your kanji app shouldn't have listed "nitsu" as an on-yomi for
日 is sometimes read
ニッ but as a gemination from
ニチ so really that's the same one on-yomi.
Building on expecting
日本 to be read with the on-yomi of its kanji, and gemination being omnipresent in modern Japanese, you should have expected it to be possibly read "nippon" or "jippon".
Only remains "nihon", which indeed is an oddity and warrants a question here.