Cournot equilibrium question
To answer your question I will assume that 

$\bf{A1}$ firm 2 always "trust" in the output reported by firm 1, and

$\bf{A2}$ firm 1 always "keep its word" if announces an output.

Without $\bf{A1}$ and $\bf{A2}$ I think you need more information to solve the game.

Based on how the question is written, at the first period firm 1 has the opportunity to whether announce or not its output. So, lets say that firm 1 must to chose between $\{A, NA\}$ ($A$ for announce and $NA$ for not announce) at $t=1$. 

Then, if firm 1 chose $A$ the resulting game will be the same as point i) of your question. In the same way, if firm 1 chose $NA$ the resulting game is the point ii) of your question. 

Finally, you only need to obtain the utility of firm 1 for both cases to know what is the best action for firm 1 at $t=1$. The subgame perfect equilibrium must to include the action of firm 1 at $t=1$ and the quantities of both firms at $t=2$.

PS: In point ii) you have a mistake, the Cournot game is symmetric so there is impossible to get different quantities in a Nash equilibrium. (sorry for my bad english)