A $(v,k,λ)$-BIBD $(X,\mathcal B)$ can be nested if there is a mapping $φ:\mathcal B\rightarrow X$ such that $(X,\{B\cup\{φ(B)\}\mid B\in\mathcal B\})$ is a $(v,k+1,λ+1)$-packing. A $(v,k,λ)$-BIBD has a (perfect) nesting if and only if its incidence graph has a harmonious (exact) coloring with $v$ colors. This paper shows that given any positive integers $k$ and $λ$, if $k\geq 2λ+2$, then for any sufficiently large $v$, every $(v,k,λ)$-BIBD can be nested into a $(v,k+1,λ+1)$-packing; and if $k=2λ+1$, then for any sufficiently large $v$ satisfying $v \equiv 1 \pmod {2k}$, there exists a $(v,k,λ)$-BIBD having a perfect nesting. Banff difference families (BDF), as a special kind of difference families (DF), can be used to generate nested designs. This paper shows that if $G$ is a finite abelian group with a large size whose number of $2$-order elements is no more than a given constant, and $k\geq 2λ+2$, then a $(G,k,λ)$-BDF can be obtained by taking any $(G,k,λ)$-DF and then replacing each of its base blocks by a suitable translation. This is a Novák-like theorem. Novák conjectured in 1974 that for any cyclic Steiner triple system of order $v$, it is always possible to choose one block from each block orbit so that the chosen blocks are pairwise disjoint. Novák's conjecture was generalized to any cyclic $(v,k,λ)$-BIBDs by Feng, Horsley and Wang in 2021, who conjectured that given any positive integers $k$ and $λ$ such that $k\geq λ+1$, there exists an integer $v_0$ such that, for any cyclic $(v,k,λ)$-BIBD with $v\geq v_0$, it is always possible to choose one block from each block orbit so that the chosen blocks are pairwise disjoint. This paper confirms this conjecture for every $k\geq λ+2$.