For the first one, I did the example myself and used g = 9.8 and got your value. Using a value of g = 9.805, I got 346.537, which rounded gives the desired result. However, I looked it up and got a value of 9.806 from Gravity of Earth - Wikipedia, the free encyclopedia (third paragraph).

If you take 9.789 at the equator, you get 345.97

And if you take 9.832 at the poles, you get 347.492

So I guess you should expect a small variation in your answer, depending on the exact constants used.

For the second part, it is somewhat ambiguous. Which way is the hemisphere facing?