  Mass measurements of fission and projectile fragments, produced via $^{238}$U
and $^{124}$Xe primary beams, have been performed with the multiple-reflection
time-of-flight mass spectrometer (MR-TOF-MS) of the FRS Ion Catcher with a mass
resolving powers (FWHM) up to 410,000 and an uncertainty of $6\cdot 10^{-8}$.
The nuclides were produced and separated in-flight with the fragment separator
FRS at 300 to 1000 MeV/u and thermalized in a cryogenic stopping cell. The
data-analysis procedure was developed to determine with highest accuracy the
mass values and the corresponding uncertainties for the most challenging
conditions: down to a few events in a spectrum and overlapping distributions,
characterized only by a broader common peak shape. With this procedure, the
resolution of low-lying isomers is increased by a factor of up to three
compared to standard data analysis. The ground-state masses of 31 short-lived
nuclides of 15 different elements with half-lives down to 17.9~ms and count
rates as low as 11 events per nuclide were determined. This is the first direct
mass measurement for seven nuclides. The excitation energies and the
isomer-to-ground state ratios of six isomeric states with excitation energies
down to about 280~keV were measured. For nuclides with known mass values, the
average relative deviation from the literature values is $(2.9 \pm 6.2) \cdot
10^{-8}$. The measured two-neutron separation energies and their slopes near
and at the N=126 and Z=82 shell closures indicate a strong element-dependent
binding energy of the first neutron above the closed proton shell Z=82. The
experimental results deviate strongly from the theoretical predictions,
especially for N=126 and N=127.
