Regarding your first question, kanji have different readings known as the onyomi (sound reading taken from the pronunciation of the Chinese characters) and the kunyomi (meaning reading taken from the Japanese word represented by the Chinese character) readings. They’re a fundamental part of learning kanji, and it’s not uncommon for kanji to have multiple readings of both types. There are a few general rules (usually compound words use the onyomi reading, for example), but you’ll need to pay special attention to the correct reading. WaniKani has an article on this topic found here: https://knowledge.wanikani.com/wanikani/japanese/onyomi-kunyomi/.
Your third question is related to the first (しん and がい are onyomi readings while こころ and そと are kunyomi readings). When you input the wrong reading, WaniKani will nudge you in the right direction with a gentle reminder.
As for your second question, while those words mean the same thing, they technically have different functions, but I don’t sufficiently understand the distinction myself. 半 is a noun, noun suffix, and noun prefix, while 半分 is a noun and an adverbial noun.
EDIT: You should run into 生 soon, as it is a Level 3 Kanji, and it’s an excellent example because it has a number of onyomi (せい, しょう) and kunyomi readings (い・きる, う・む, は・える, and なま [the interpunct separates the kanji’s pronunciation from its accompanying hiragana]).
Each of the kunyomi readings has a different meaning associated with “life” (“to live”, “to give birth”, “to grow”, and “live” [as in, “live bait”], respectively), while the onyomi readings are used in compound words like 人生 (じんせい, “one’s life”) and 一生 (いっしょう, “lifelong”).