"on a purpose" does not make sense here. "Its purpose" is correct. It means "the reason or objective for the research". "On purpose" means "deliberately".

no, can substitute with "aims"

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Without context, the statement is unclear as written. Both ‘delivering’ and ‘purpose’ sound unnatural. If it’s her own research, it would be odd to not know its purpose. Natural things to say with different meanings: My colleague is sending you the data (that) you asked her to collect. She wants to know how you will use it. My colleague is sending you some research (that) she found. She thinks you might be able to use it somehow. A colleague is sending you some research that she’s done. She wants your opinion as to whether it’s useful or not.