TRomano's explanation of the first two sentences doesn't really need improvement, but I will rephrase to reinforce.
1. She had lived with the family since she was born.
2. She has lived with the family since she was born.
The first sentence is looking backwards from a point in the past. Christina lived with the family from her birth until some date that is in the past, and we would expect to find it in the context. This sentence says absolutely nothing about where Christina lived after that date in the past up until the present.
The second sentence establishes an unbroken timeline from Christina's birth to the present timeframe, during which she lived at home.
3. There have been many great inventions or things that changed the way we live.
4. There are many great inventions or things that changed the way we live.
The third sentence notes that inventions have occurred in the past that changed how humans lives. These inventions may or may not still be in use - the important thing is that they were significant at some point in the history of human development. You could refer to the telegraph or the cell phone in this way: The telegraph and the mobile phone changed the way we live. The telegraph is no longer used; the mobile phone is. Each in their own time had a significant impact on human societies.
The fourth sentence is not great. The best interpretation is that there are technologiesstill in use that changed human's lives at some point in the past. (And may or may not continue to do so.) It would be better expressed as There are many great inventions or things that change the way we live.