You'll need some kind of database for the questions, mySQL would do there.
You'll need a server-side scripting language to connect to the database, offer up random questions, submit viewer answers back to the server and allow access if the answers are right. PHP should be able to handle that.
I would say at minimum a basic knowledge of mySQL and HTML with an intermediate to advanced understanding of PHP would do it.
The code isn't going to be something you'll be able genereate using DW and I suspect there isn't going to be much online that you could copy and paste to get the results you want. This would need to be done by hand for the most part.
You could do this without a database, but you could't do without the server-scripted part. You would just test for the answers in the scripting.
But I have to ask - why is the quiz so stringent? Seems to me that just a couple of questions would be good enough....
So sorry to hear of your condition. What you're trying to do is not trivial unless you're already familiar with PHP/ MySQL and accepting/ validating input on forms. Dreamweaver will help but you'll really need to understand what it's generating for you.
May I suggest a non-automated solution might be more straight forward. For example you could leave sealed letters with the executor of your will, or a trusted friend or attorney, with instructions on when/ how to deliver them.