Can Captivate be used for that kind of Quizzes ?

It is my right, I am just a user, to protect myself. Moreover the download was a SWF-file. I watched bart of that Youtube video, very boring. Do you really label this as eLearning?

As for your questions:

1. You can have a button to pop up more information on quiz slides. I have blogged about that many years ago. You'll need to use a shape button and the popup will need a shared action. You didn't tell if you want a responsive project. For a responsive project, created with Fluid Boxes, I would use a multistate object for the popup. The popup will not be 'floating' in the sense I see that term, but it can have audio, images, text...
2. No automatic mails, but automic warnings is not a problem. Mails in a LMS or webbrowser always need an interaction of the learner. You don't even know if the learner has set up a mail client, nor which mail client.
3. You can create custom questions with the checkboxes learneing interactions. Have examples on my blog. You didn't sepcifiy if you want multiple attempts on question level, nor if you want a Review/Retake possibility.
4. Branching is not a problem with Captivate, but you have to explain what you mean by 'braniching quiz capabilities' to give you a more detailed answer.
5. Scoring of course, do you want to transfer it to a LMS?