The elliptic ($\upsilon_{2}$) flow of prompt D$^{0}$ mesons, together with K$^{0}_{S}$, $\Lambda$, $\Xi$, and $\Omega$ in high-multiplicity pPb collisions at 8.16~TeV, is presented. The data are collected with the CMS detector at the LHC from the rapidity interval $-1.46 < y_{cm} < 0.54$ and transverse momentum range 1.5 $< \mathrm{p_{T}} <$ 8~GeV. The results are compared to those from the 30--50\% centrality PbPb data at 5.02~TeV. A mass-ordering behavior with a stronger $\upsilon_{2}$ of lighter species for $\mathrm{p_{T}} <$ 2~GeV is observed. The $\upsilon_{2}$ scaled to the number of constituent quarks vs the transverse kinetic energy per constituent quark shows that the D$^{0}$ scaled $\upsilon_{2}$ values in pPb collisions are smaller than those of light-flavor particles. Such an effect is not observed in PbPb collisions indicating a weaker collectivity of charm quarks than the one of light-flavor quarks, and a weaker coupling between heavy quarks and a possibly formed quark-gluon plasma droplet. The $\upsilon_{2}$ of prompt J/$\psi$ mesons in high-multiplicity pPb collisions at 8.16~TeV is also measured. The J/$\psi$ mesons are reconstructed via the dimuon channel with 1.4 $< \mid y \mid <$ 2.4 and 2 $< \mathrm{p_{T}} <$ 8~GeV. This observation provides the most direct evidence for the presence of charm quark collectivity in pPb collisions. Comparison with $\upsilon_{2}$ of D$^{0}$ and strange hadrons allows a strong constraints on the dynamics of charm quarks produced in small hadronic collision systems with high multiplicities. Additionally, the standard and the subevent cumulant method is used to measure correlations between the $\upsilon_{2}$ and triangular ($\upsilon_{3}$) flow, and between the $\upsilon_{2}$ and quadrupole ($\upsilon_{4}$) flow in pPb collisions up to very low multiplicities. At high multiplicities, all methods give similar results showing that non-flow is not the dominant in this region, while at low multiplicities, the subevent method allows to strongly suppress the non-flow contribution and reveals the pure collectivity.