  We report a comprehensive analysis of the light and strange disconnected-sea
quarks contribution to the nucleon magnetic moment, charge radius, and the
electric and magnetic form factors. The lattice QCD calculation includes
ensembles across several lattice volumes and lattice spacings with one of the
ensembles at the physical pion mass. We adopt a model-independent extrapolation
of the nucleon magnetic moment and the charge radius. We have performed a
simultaneous chiral, infinite volume, and continuum extrapolation in a global
fit to calculate results in the continuum limit. We find that the combined
light and strange disconnected-sea quarks contribution to the nucleon magnetic
moment is $\mu_M\,(\text{DI})=-0.022(11)(09)\,\mu_N$ and to the nucleon mean
square charge radius is $\langle r^2\rangle_E\,\text{(DI)}=-0.019(05)(05)$
fm$^2$ which is about $1/3$ of the difference between the $\langle
r_p^2\rangle_E$ of electron-proton scattering and that of muonic atom and so
cannot be ignored in obtaining the proton charge radius in the lattice QCD
calculation. The most important outcome of this lattice QCD calculation is that
while the combined light-sea and strange quarks contribution to the nucleon
magnetic moment is small at about $1\%$, a negative $2.5(9)\%$ contribution to
the proton mean square charge radius and a relatively larger positive
$16.3(6.1)\%$ contribution to the neutron mean square charge radius come from
the sea quarks in the nucleon. For the first time, by performing global fits,
we also give predictions of the light and strange disconnected-sea quarks
contributions to the nucleon electric and magnetic form factors at the physical
point and in the continuum and infinite volume limits in the momentum transfer
range of $0\leq Q^2\leq 0.5$ GeV$^2$.
