  Modern Multimessenger Astronomy is a powerful instrument for performing
cosmological crucial tests of the Standard Cosmological Model in the wide
redshift interval up to $z \sim 10$. This is principally important for
discussion related to discrepancies between local and global measurements of
cosmological parameters. We present a review of multimessenger gamma-ray burst
observations currently conducted and planed for THESEUS$-$BTA cooperative
program. Such observations give a unique opportunity to test the fundamental
foundations of cosmological models: gravitation theory; cosmological principle
of homogeneity and isotropy of large-scale distribution of matter; and space
expansion paradigm. Important role of various selection effects leading to
systematic distortions of true cosmological relations is discussed.
