No not really "built in" or "in built" is only used for buildings or machines etc. To be jealous is a characteristic of herS. You pluralise her in that sentence to make it similar to the 's possessive comma of ownership. It is typical of her to be jealous. To be jealous is a characteristic of herS. It is typical of her to be jealous. You could ask another question why is there an S on first sentence and not on the second sentence. I have completely forgotten, it being a long time since I have been in an academic environment.

No. You could perhaps say "is a built-in quality of hers". But jealousy isn't a quality. Qualities should be positive. It's not something I would ever say, so it's hard to think of a natural alternative. Perhaps "To be jealous is natural to her"?

Hello Mona! I don't think it is natural. You can say "she is being jealous.." or "jealousy is a big part of her personality".

To answer the question you have been asked. "Built" is something that people do and make not a quality that humans have. The sentence is awkward at the very least. A person can have an inbred quality or a quality passed on by upbringing either good or bad.