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The F Test and Multiple Regression Model for Two Independent Variable

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Suppose in the following model

y_i = a_0 + (a_1)(x_1i) + (a_2)(x_2i) + u_1 i = 1,2,....., n

I want to test whether both slope coefficients are zero. In order to derive the restricted residual sum of squares, it is necessary to estimate the following model:

y_1 = a_0 + u_i

Firstly, how can I show that the least squares estimator of a_0 is the sample mean of y_i?

Secondly, how do I derive the relationship between the F test which tests the null given above and R^2?

What are the advantages and disadvantages of R^2? How do I go about explaining if the standard errors of the residuals is better?

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