Here are some synonyms for inquisitive:
* Curious
* Questioning
* Inquiring
* Exploratory
* Prying (sometimes has a negative connotation)
An inquisitive person is often:
* Asking lots of questions
* Seeking information
* Interested in learning new things
* Paying close attention to details
For example:
* "The inquisitive child asked endless questions about the world around them."
* "Her inquisitive nature led her to travel to many different countries."
* "The reporter's inquisitive line of questioning revealed the truth about the scandal."