(a)

The test is right.

You are interested in deviations where x is too high, so this is a 1 tailed test.

0.0088 is far lower than the significance level (0.05), so reject H0. Be very careful about saying you accept H1. Saying H0 is false isnotthe same as saying H1 is true, except in special cases where H1 is "H0 is false".

I'm not familiar with the "z-score" notation so i dont know if that is the same as your answer

(b)

yes