How can I generally determine which bonds are longest/shortest in a molecule?
Because atomic radii of elements tend to decrease across a period (source), and bond length increases with atomic radius, the bond lengths are expected to decrease in the following order: C (C-C bond) > B, D (C-N) > A (C-F).

The difference between B and D is that in D, the nitrogen is $sp^3$-hybridized, while in B, it is $sp^2$-hybridized due to conjugation of its lone pair with the aromatic ring 2. This results in partial double bond character of the C(ring 2)-N bond, similar to aniline:



More $s$ character leads to shorter bonds, and therefore the C-N bond B is shorter than D.

In summary, the bond lengths decrease in the following order: C > D > B > A.