I'm new with Magento 1.9 and I'm trying to setup my solution to reach these goals maybe with an extension/other kind of solution that would allow:
Is there any solution for this?
1) Is possible. Magento can't configure a parent or child store but you can handle several stores with problems. I've made a fast search and I've found, for example, this tutorial: https://www.youtube.com/watch?v=8Ms2AFmiE0g (there are several more)
2) You can choose if a product is available on every website.
3) I guess that when you say Store in Magento is Website. In this case you'll be able to separate users per Website. If a custoemr wants to buy on 2 or more Websites it will need to regiestr as many times as Websites.
4) Yes, you can have differents payment methods or the same payment method with different credentials per Website.
5) Magento 1 CE isn't multitenant by default. You'll need to buy or make some module to handle that kind of restrictions. Also, the "need to accept" maybe isn't on those modules neither.
I guess that you need to find a solution for point 5. The rest of requirments are, basically out-of-the-box features and configuration.