reading the output of a r regression analysis 

1) How much does gender influence the trust in people according to the regression output in Table 1?

When the question asks "How much?", I will interpret as the percentage of the variability of trust that can be explained by gender. The $R^{2} $ is the statistic to use for this interpretation. $R^{2} $ =0.001 = 0.1%
Therefore 0.1% of the variability of trust in people is explained by gender and 99.9% of the variability of trust in people is explained by other factors.

2) What is the t-value of the coefficient of gender in Table 1?

$F(1,k)=t^{2} (k)$ where k is the degrees of freedom. Since the gender coefficient is negative, the t statistic will also be negative.  Therefore $t(47366)=-\sqrt{F(1,47366)} = -\sqrt{34.437} =-5.868$ 

3) Is the coefficient of gender in Table 1 significantly different from zero? Tip: Do not gaze for stars.

The p-value for this t-statistic $P(|t| > 5.868)$ is less than 0.0000001, so the coefficient for gender is clearly and significantly different from zero.

4) Is women?s trust in people larger or smaller than zero according to the regression output in Table 1?

The regression equation is TRUST = CONSTANT + WOMAN where
WOMAN = 1 for women and WOMAN = 0 for non-women.
For a woman, TRUST = 0.029 - 0.054 = -0.027
Therefore, women?s trust in people is smaller than zero.