  Less than one percent of the discovered small solar system objects have
highly inclined orbits ($i>60^{\circ}$), and revolve around the Sun on
near-polar or retrograde orbits. The origin and evolutionary history of these
objects are not yet clear. In this work we study the surface properties and
orbital dynamics of selected high-inclination objects. BVRI photometric
observations were performed in 2019-2020 using the 2.0m telescope at the
Terskol Observatory and the 2.6m telescope at the Crimean Astrophysical
Observatory. Additionally, we searched for high-inclination objects in the
Sloan Digital Sky Survey and Pan-STARRS. The dynamics of the selected objects
was studied using numerical simulations. We obtained new photometric
observations of six high-inclination objects. All of the objects have similar
$B-V$, $V-R$, $R-I$ colours, which are close to those of moderately red TNOs
and grey Centaurs. The photometric data that were extracted from the all-sky
surveys also correspond to moderately red surfaces of high-inclination objects.
No signs of ultra-red material on the surface of high-inclination asteroids
were found, which supports the results of previous works. The comet C/2018 DO4
(Lemmon) revealed some complex morphology with structures that could be
associated with particles that were ejected from the cometary nucleus. For
objects 2013 LU28, 2015 KZ120, and 2020 EP we estimated future and past
lifetimes on their orbits. It appears that the orbits of considered objects are
strongly chaotic, and with the available accuracy of the orbital elements no
reliable predictions can be made about their distant past or future. The
lifetimes of high-inclination objects turned out to be highly non-sensitive to
the precision of the orbital elements, and to the Yarkovsky orbital drift.
