11. Mihi quaerenti opus est mente acri ut haec intellegam.
To me when questioning the need is for a sharp mind that I might understand this.
I had difficulty with this one too. The problem for me was getting quaerentī
into smooth English. Without it, the sentence is I need a sharp mind [or a keen intellect] to understand this.
Your literal translation looks fine to me; the issue is how to polish it into a form that we might speak. It's difficult with a short sentence like this that gives no idea of its context, and I don't worry too much these days, so long as I am reasonably happy that I've understood the syntax and vocab. Maybe Since I'm the one asking, I need a sharp mind...etc
12. Semper erimus rerum omnium memores de rei publicae spebus.
Always we shall keep in mind everything that concerns the hopes for the republic.
Maybe "of the republic [state]" might be better than "for the republic", since reī publicae
is perhaps more likely to be genitive than dative.