• For number (1), use $\Sigma M_D = 0$ to solve for $R_1$ and $\Sigma M_B$ for $R_2$
• For number (5), I think the instruction is not worded precisely because the flexural capacity is already given which is 27.6 MPa. I think the question is about the maximum moment capacity, it is practical to interpret it this way. With this, just use the flexure formula for rectangular section which is $f_b = \dfrac{6M}{bd^2}$, and solve for M while holding fb at 27.6 MPa. The value of M will be the maximum moment capacity of the beam.
• Compare the maximum moment you get from from (5) to the maximum moment you get in you shear and moment diagram which are the actual moments. Of course if the largest actual moment is larger than that in number (5) then your section is inadequate and you need a deeper beam, re-design your beam with adequate $d$ per instruction. However if the largest moment in your diagram is less than or equal to the moment in (5) then no need to redesign because the section is already good to go in terms of moment capacity