  We systematically analyze the full angular distribution in $D \to P_1 P_2 l^+
l^-$ decays, where $P_{1,2}=\pi,K$, $l=e,\mu$. We identify several null tests
of the standard model (SM). Notably, the angular coefficients $I_{5,6,7}$,
driven by the leptons' axial-vector coupling $C_{10}^{(\prime)}$, vanish by
means of a superior GIM-cancellation and are protected by parity invariance
below the weak scale. CP-odd observables related to the angular coefficients
$I_{5,6,8,9}$ allow to measure CP-asymmetries without $D$-tagging. The
corresponding observables $A_{5,6,8,9}$ constitute null tests of the SM. Lepton
universality in $|\Delta c| =|\Delta u|=1$ transitions can be tested by
comparing $D \to P_1 P_2 \mu^+ \mu^-$ to $D \to P_1 P_2 e^+ e^-$ decays. Data
for $P_1 P_2=\pi^+ \pi^-$ and $K^+ K^-$ on muon modes are available from LHCb
and on electron modes from BESIII. Corresponding ratios of dimuon to dielectron
branching fractions are at least about an order of magnitude away from probing
the SM. In the future electron and muon measurements should be made available
for the same cuts as corresponding ratios $R_{P_1 P_2}^D$ provide null tests of
$e$-$\mu$-universality. We work out beyond-SM signals model-independently and
in SM extensions with leptoquarks.
