In my culture [white collar North American office jobs, over 30 years old, English speaking], it is never appropriate to ask anyone their salary, ever, in public or in private. Not someone below you, not someone above you, no-one. Occasionally there are exceptions but they must always be worded carefully:
If I were to rise to a position like yours, what kind of salary could I expect?
What's the ratio between the highest and lowest salaries in our firm?
What percentage of the total salary expense in this company goes to executives, and what percentage to those who [make what we sell, or bill for our time, or whatever]?
How much do they pay you to do this?
As for asking his job responsibilities, it's good that you want to know that. Many people have no idea what the executives above them do, or think they know and don't really think it's important. I recommend you start below the CEO though. Much of what you do is assigned to you in order for your direct manager to achieve some goals that were set by the company. Say you're a sales rep, and your manager is head of sales. Someone decided "we should sell 5% more this year" and gave that to your manager as a goal. Your manager in turn may have asked you to sell 7% more this year, knowing that some other new hire is unlikely to sell more than the new hire he or she replaced. [Or someone decided that a way to raise sales would be to release version 2.7 of something, and it's your job to write, test, document or whatever this new version 2.7.]
In the same way, the reason your manager was asked to raise sales 5% in a particular division is that someone else was asked to raise revenue 6% overall, and that's because someone else was asked to raise profit 7% overall, and so on. As you look up the chain you'll understand that executives deal in a different reality than line workers, and each contributes to the whole. It's really common for a CEO not to be able to make the product the company sells, or even use it. That doesn't make them unqualified - painting is not the same as running an art gallery, cooking is not the same as running a restaurant, etc.
If you're genuinely curious what a CEO does all day, there are lots of ways to learn about it. Chatting with your manager about what a manager does all day, then asking about a director, a VP, a senior VP etc can be very illuminating. So can reading web sites or magazines for executives. If your agenda is more "I can't believe this knucklehead gets 10 times my salary and couldn't even launch Visual Studio to save his life", tread VERY carefully. You're probably not right, but more importantly even if you are, there is essentially nothing for you to gain by being right in that opinion.