As for the second question, the answer is that pointwise limits implies limits in functor categories, by the ``limit with parameters'' theorem (Theorem V.3.1 of Mac Lane).

Because in general $f$ is mono iff there is a pullback of $f:\rightarrow\cdot\leftarrow:f$ consisting of unit arrows (exercise in Mac Lane, p. 72), I think this also answers the first question: pointwise mono implies mono.

This is only a partial answer. Regarding your first question (mono/epi iff pointwise mono/epi): At least for the case where the target category $\mathcal{D}$ is $\mathbf{Set}$, it is true that pointwise mono/epi implies mono/epi, see p. 91 of the 1998 edition of Mac Lane.

As for the second question, the answer is that pointwise limits implies limits in functor categories, by the ``limit with parameters'' theorem (Theorem V.3.1 of Mac Lane).

This is only a partial answer. Regarding your first question (mono/epi iff pointwise mono/epi): At least for the case where the target category $\mathcal{D}$ is $\mathbf{Set}$, it is true that pointwise mono/epi implies mono/epi, see p. 91 of the 1998 edition of Mac Lane.

As for the second question, if I understand correctly, the answer is that pointwise limits implies limits in functor categories, by the ``limit with parameters'' theorem (Theorem V.3.1 of Mac Lane).

(I am in a rush right now, but I hope this answer makes any sense :))

As for the second question, the answer is that pointwise limits implies limits in functor categories, by the ``limit with parameters'' theorem (Theorem V.3.1 of Mac Lane).

Because in general $f$ is mono iff there is a pullback of $f:\rightarrow\cdot\leftarrow:f$ consisting of unit arrows (exercise in Mac Lane, p. 72), I think this also answers the first question: pointwise mono implies mono.