  We study milliarcsecond-scale properties of the persistent radio counterpart
to FRB 121102 and investigate the spectro-polarimetric properties of a bright
burst. For the former, we use European VLBI Network (EVN) observations in 2017
at 1.7 and 4.8 GHz. For the latter, we re-analyse the 1.7-GHz data from the
100-m Effelseberg telescope taken in 2016. These observations predate other
polarimetric studies of FRB 121102, and yield the highest burst Faraday
rotation measure (RM) to date, RM = 1.27*10^5 rad m^-2, consistent with the
decreasing RM trend. The fractional polarization of the burst emission is 15%
at 1.7 GHz. This can be reconciled with the high fractional polarization at
higher frequencies if the Faraday width of the burst environment is 150 rad
m^-2 - a bare 0.1% of the total Faraday rotation. The width may originate from
minor non-uniformities in the Faraday screen, or from effects in the emitting
region itself. The upper limit on the persistent source size is 1 pc, barely
consistent with a young supernova (SN) scenario. The flux variability limit of
<10% is not in favor of the young SN scenario, and challenges other
interpretations as well. The fractional polarization of the faint persistent
source is constrained at <25% at 4.8 GHz ruling out a common origin with the
highly polarized individual bursts.
