About "There" "They're" and "Their"

I find that many people make mistakes when using There. Their. and They're....
I understand that these 3 words/phrases sound similar and people tend to mix them up. When spoken, it doesn't make much of a difference regarding which one you've actually used, however, when a person is writing something, it is crucial to use the correct one. Other people might still understand what you are trying to say when you've used an incorrect word, however, their opinion of you may not be as well as you'd hope.

1. There, this word relates to the location of something. For example, "I see an icecream store over THERE." or "There she is! I've finally found her".

2. They're, this is actually made up of 2 words, THEY ARE. This relates to the state/disposition that the subjects are being commented upon. For example, "They're the nicest people that I have met." or "They're hungry, get them something to eat".

3. Their, this is used when one's talking about the possession of someone. An example would be ... "This is their bike, please do not break it."

It just occurred to me that ... most Chinese people don't have the problem of mixing up these 3 ... but the children that have grown up here often do. I guess people from China just learn way more grammar in the earlier years than the people who grow up in an English speaking country such as Canada.

thx