Is there a verification of the solar system barycenter as it is theoretically determined? The barycenter of our solar system is not the sun, but a changeable location outside of the center point of the sun. A often used diagram of that relation is shown below, originated from the Wikipedia article. 

Does exist one or more practical quite observations that confirm the accordance of the real changing of position of the barycenter of the solar system in relation to the center point of the sun with the theoretical results?
Yes, measurements do exist. JPL takes very precise observations of many objects in the solar system and tries to obtain a location for the solar system barycenter.

The solar system barycenter is a hot topic especially in terms of PTA's, or pulsar timing arrays - we need precise a precise location for the solar system barycenter to do work with these pulsar timing arrays. I'll put some links at the bottom as well to help.

JPL does get its own calculations of the solar system barycenter, and AFAIK, they do this with use of what they call the Solar System Ephemeris - see more here and here, at their Solar System Dynamics page. They get precise locations of many objects in the solar system and then try to calculate a center of mass from there.

A cool walk-through of the effect of the eight planets and Pluto (and some other stuff) on the movement of the Sun.