  We investigate the effectiveness of blind surveys for radio sources and
galaxy cluster thermal Sunyaev-Zel'dovich effects (TSZEs) using the four-pair,
beam-switched OCRA-f radiometer on the 32-m radio telescope in Poland. The
predictions are based on mock maps that include the cosmic microwave
background, TSZEs from hydrodynamical simulations, and unresolved radio
sources. We estimate the effects of source clustering towards galaxy clusters
from NVSS source counts around Planck-selected cluster candidates, and include
appropriate correlations in our mock maps. The study allows us to quantify the
effects of halo line-of-sight alignments, source confusion, and telescope
angular resolution on the detections of TSZEs.
  We perform a similar analysis for the planned 100-m Hevelius radio telescope
(RTH) equipped with a 49-beam radio camera.
  We find that RT32/OCRA-f will be suitable for small-field blind radio source
surveys, and will detect $33^{+17}_{-11}$ new radio sources brighter than 0.87
mJy at 30~GHz in a 1 deg$^2$ field at $>5\sigma$ CL during a one-year,
non-continuous, observing campaign, taking account of Polish weather
conditions. It is unlikely that any galaxy cluster will be detected at
$3\sigma$ CL in such a survey. A $60$-deg$^2$ survey, with field coverage of
$2^2$ beams per pixel, at 15 GHz with the RTH, would find <1.5 galaxy clusters
per year brighter than 60 $\mu$Jy (at $3\sigma$ CL), and would detect about
$3.4 \times 10^4$ point sources brighter than 1 mJy at $5\sigma$ CL, with
confusion causing flux density errors $\lesssim 2\%$ (20%) in 68% (95%) of the
detected sources.
  A primary goal of the planned RTH will be a wide-area ($\pi$~sr) radio source
survey at 15 GHz. This survey will detect nearly $3 \times 10^5$ radio sources
at $5\sigma$ CL down to 1.3 mJy, and tens of galaxy clusters, in one year of
operation with typical weather conditions. ABRIDGED
