  Photon-photon reactions and the production of J/$\psi$ meson through
photonuclear reactions have been extensively studied in ultra-peripheral
heavy-ion collisions, in which the impact parameter is larger than twice the
nuclear radius. In recent years, coherently photoproduced J/$\psi$ and dilepton
production via photon-photon interactions have also been observed in
nucleus-nucleus (A-A) collisions with nuclear overlap. The former can help to
constrain the nuclear gluon distributions at low Bjorken-$x$ and high energy,
while the latter could be used to further map the electromagnetic fields
produced in heavy-ion collisions. In addition, these measurements can shed
light on the theory behind photon-induced reactions in A-A collisions with
nuclear overlap, including possible interactions of the measured probes with
the formed and fast expanding quark-gluon plasma. Since the produced quarkonium
is expected to keep the polarization of the incoming photon due to $s$-channel
helicity conservation, the photoproduction origin of the J/$\psi$ yield excess
at very low transverse momentum, $p_{\rm T}$, can be confirmed by the
measurement of the J/$\psi$ polarization. The ALICE detector can perform
quarkonium production measurements at both mid ($|y|<0.9$) and forward
($2.5<y<4$) rapidities down to $p_{\rm T} = 0$. In the following, the new ALICE
measurements of the J/$\psi$ $y$-differential cross section and the first
polarization results of coherently photoproduced J/$\psi$ via the dimuon decay
channel at forward rapidity in Pb-Pb collisions at $\sqrt{s_{NN}}=$ 5.02 TeV
are reported. Additionally, the measurement of an excess with respect to
expectations from hadronic production in the dielectron yield, at low mass and
$p_{\rm T}$, at midrapidity in Pb-Pb collisions at $\sqrt{s_{NN}}=$ 5.02~TeV,
is presented. The results are compared with available theoretical models.
