does it work with my daughter ???? she is 9 years old

It is recommended for aging women/men that are thinning or losing their hair. I don not believe it's for young people. Why would you use it on a child? if they are having scalp problems/losing hair - see a doctor!

what is difference between system 1 & 2?

Nioxin's Systems 1 & 2 are designed for users with natural hair (no hair color, bleach or chemical processes on the hair). System 1 is for users with normal to light thinning hair, while System 2 is for users with progressed thinning hair.

Does this come with a corresponding pump?

Great question I would be happy to assist you with. No, this does not come with a pump however, you can purchase a pump separately. https://www.amazon.com/Pump-Nioxin-liter-33-8-bottles/dp/B07CVM36HC I hope this answered your question today. Have a Beautiful Day!

Can you use with Rogaine?

Thank you for reaching out to us at Nioxin and asking this product question today. We do not recommend using our products with Rogaine as we are two different brands and lines not researched or developed together. When using Nioxin we recommend only using our Nioxin System Kit and supporting products together only. You never cross brands or lines when it comes to professional systems. I hope this was of help and answered your question today. If you have more Nioxin questions or would like a free consultation with one of our Licensed Professionals we would be happy to do this for you. Give us a call at 1-800-935-5273. Have a Wonderful Nioxin Hair Day!