Modern Multimessenger Astronomy is a powerful instrument for performing crucial tests of the Standard Cosmological Model in the wide redshift interval up to z similar to 10. This testing 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 performed and planed for THESEUS-BTA cooperative program. Such observations provide 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.