How do the Japanese speakers pronounce the Chinese charactors ? Do they need to remember all the pronounciations of a single Chinese Charactor ? And then what ? Try to match to sigure out the actual meaning ?
They may be written the same way (for the ones that are used in Japanese, at least), and have the same Unicode assignments; but in the context of Japanese text, they are Japanese characters - i.e., 漢字{かんじ}, not 漢字{Hànzì}. Just like how chat can either be English for a casual conversation or French for a cat, and in a French text, they are French characters.
Native speakers learn Japanese pronunciation just like those of any other native language: by immersion since childbirth (and reading of kanji by being schoolchildren and being immersed in real-world text the rest of their lives). Like in Chinese, in Japanese the characters fundamentally encode meaning. (They may also encode an on-reading. These are readings that are influenced by the Chinese reading. For example, かん is supposed to sound like Hàn, and じ like zì. But the word was imported into the Japanese language many centuries ago, and there has been some drift since then. Anyway, a common example is 語, which shares its on-reading of ご with the 五 in the top right.)
Typically, kanji in a Japanese text will either cluster in groups of four (四字熟語{よじじゅくご} - literally four-character compounds) which can be either nouns or stand-alone idioms; pair up (these are normally nouns, and normally use the most common on-reading for each); or else are followed by okurigana (indicating a verb or an i-adjective, possibly with further inflection).
So, for 自分 we recognize a common word じぶん, and 分 is simply read ぶん (the on-reading is ふん, which becomes voiced by what is called 連濁 {れんだく}). For 分かる, we again recognize the common verb, where 分 is read わ. Because it's a verb, the kun-reading (native Japanese reading) is more likely. We recognize it as a verb because of the okurigana.
In a japanese verb/adj, what does the Chinese character mean in a Japanese speaker's eyes ? For Chinese speaker it means and relates to something.
To my understanding, as a rule it has a similar meaning. The root meaning of 分 has to do with splitting something up. Nouns containing it typically have a meaning of some kind of portion of a whole. (For example, it's used to mark a minute of time, because it's a small division of an hour - just like the English word minute, which shares a root with the adjective, minute (different pronunciation!), meaning small.) The verb meaning, typically glossed with words like "understand" or "become clear", is related: a complex thing becomes understandable when it is broken down into pieces.
This meaning-awareness can inform reading. For example, 食欲{しょくよく} "appetite" uses the very commonly seen 食 of 食｛た｝べる and the 欲 of 欲{ほ}しい ("usually kana" per Jisho, but you'll at least see it all the time if you input text with an IME). So to pronounce it, we need to think of words that have the related meanings (eating/food and desire), and then we come up with one that can plausibly match known readings of the characters (しょく is very common for 食, used in a lot of compound words). If you've already heard the word spoken and know what it means, you can recall it when you see the kanji and the concepts are called to mind.
However, I doubt that native Japanese speakers commonly think about things on this level. Being a native speaker of a language is a rather Zen practice.
For 慌ただしい and 慌しい， they are the same. But with different appearences. And the 慌 pronouse differently. Why not 慌い , which could save some writing.
Fundamentally, the pronunciation of 慌 is あわ. Over time, it became acceptable to leave out the ただ in writing, although you still pronounce it. My understanding is that, typically, those skipped characters get folded into the reading for the kanji, and they disappear completely as okurigana. However, this is an organic process that takes a long time (like spelling or pronunciation changes, or notions of acceptable grammar, in other languages). In this particular case, it would be difficult, because the reading as あわ is reinforced by the existence of the verb form 慌てる.
That said, most seemingly "extra" okurigana are there because historically, they were not "extra". i-adjectives ending in しい are the common example, as already noted; most of these indicate human emotions (think 美味｛おい}しい, 悲{かな}しい, 懐{なつ}かしい, 欲{ほ}しい...). This is considered a pretty important distinction. Another common case is 食{た}べる: it used to be that the べ could change with inflection.
