About marshallian demands
I will give a hint. To increase/decrease utility by 1 unit, you can do two things. Increase $x_1$ and $x_2$ by $\frac{1}{2}$ units and this would cost you $\frac{p_1+p_2}{2}$. The second option is changing $x_3$ by one unit that would cost $p_3$. One other option is of course using a linear combination of the above changes. If you remember from well behaved utility functions, you would like to buy things for which utility per price is higher. Now you would go for a similar reasoning here and would try to buy extra utility at a cheapest price.