You’ve already got some good replies on on’yomi and kun’yomi so I won’t go over that again. Instead, I’ll try to clarify each of your questions based on that knowledge.
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今 is pronounced いま when it’s used as vocabulary because it stands for the word いま. 今 has the reading of こん when it’s used in certain words such as 今夜, こんや, this evening.
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半分 as a word means half of something. 半 by itself is usually used with something else to denote half of it: month-and-a-half, half an egg, half time.
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こころ and しん are both actual words in Japanese that mean heart. WK shakes to let you know that it wanted the other reading. The Kanji 外 stands for the Japanese word そと. がい as a word on its own means “damage” and is represented by 害. That’s why it marks you wrong for answering がい instead of そと.Edited: See @Leebo’s clarification below.
Also, see this thread: