  We report multiwavelength observations of the gravitationally lensed blazar
QSO B0218+357 in 2016-2020. Optical, X-ray and GeV flares were detected. The
contemporaneous MAGIC observations do not show significant very-high-energy
(VHE, >= 100 GeV) gamma-ray emission. The lack of enhancement in radio emission
measured by OVRO indicates the multi-zone nature of the emission from this
object. We constrain the VHE duty cycle of the source to be < 16 2014-like
flares per year (95% confidence). For the first time for this source, a
broadband low-state SED is constructed with a deep exposure up to the VHE
range. A flux upper limit on the low-state VHE gamma-ray emission of an order
of magnitude below that of the 2014 flare is determined. The X-ray data are
used to fit the column density of (8.10 +- 0.93 stat ) x 10^21 cm^-2 of the
dust in the lensing galaxy. VLBI observations show a clear radio core and jet
components in both lensed images, yet no significant movement of the components
is seen. The radio measurements are used to model the source-lens-observer
geometry and determine the magnifications and time delays for both components.
The quiescent emission is modeled with the high-energy bump explained as a
combination of synchrotron-self-Compton and external Compton emission from a
region located outside of the broad line region. The bulk of the low-energy
emission is explained as originating from a tens-of-parsecs scale jet.
