= Solution
For a diagram shape $I$, a <functor> $F:\mathcal C\to\mathcal D$ preserves <categorical limits> of shape $I$ if every limiting cone $(L,\ell_i)$ over every diagram $D:I\to\mathcal C$ is carried to a limiting cone $(FL,F\ell_i)$ over $FD$. It reflects <categorical limits> of that shape if a cone in $\mathcal C$ is limiting whenever its image cone is limiting. These properties concern cones which are given; reflection is not an assertion that every cone in the target lifts.
Suppose $F$ is a <full and faithful functor> and the image of $(L,\ell_i)$ is limiting. A cone $(X,x_i)$ in $\mathcal C$ becomes a cone in $\mathcal D$, so there is a unique $h:FX\to FL$ with $(F\ell_i)h=Fx_i$. Fullness writes $h=Fk$ for some $k:X\to L$. Faithfulness gives $\ell_i k=x_i$, and also ensures uniqueness: two such $k$ would have the same image, by uniqueness of $h$. Hence the original cone is limiting. This proves \b[every <full and faithful functor> reflects <categorical limits>], the <limits reflected by full and faithful functors> criterion, with no essential-surjectivity requirement.
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