Everything I've written about this, above and below, are only hints. I'm not doing your homework problem for you, just poking you in the right direction. No pun intended.
The definition of the gradient is a vector function that points in the direction of the most rapid increase in a function.
To help understand this you might think of some really simple functions of x,y,z, simpler than your actual problem, where you are fairly sure you know which direction to move from a point to most rapidly increase the function. Then by hand and with Mathematica calculate the gradient and see if it matches what you think the answer should be.
Then you need to think how you might apply this understanding to your first question.
You can even try checking the answer for this. To do that move in some other direction and see if the result is not as good. Move in almost exactly the same direction as you calculate using the gradient and see if the result is very close, but still not quite as good. You are doing this to convince yourself you understand the gradient and you have the right answer.
Then for the second question you want to think of all the information you have and compare that with exactly what you need. What kind of thing would you have to have to get from what you have to what you need? When you know that then you might be able to think of a way of constructing it.
The final question I haven't thought about enough to offer any suggestion.
The forum posting software does some very odd things when it tries to desktop publish what you type. I can't offer any advice or explanation about why that is. Sorry.
