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We present an analysis of various tracers of magnetic activity for 23 solar twins which are characterized by significant scatter of lithium abundance in their atmospheres. A level of coronal and chromospheric activity has been studied from available X-ray and UV- archival data. It gives us a chance to compare coronae of solar twins of various ages with the solar case. We found a scatter in the X-ray to bolometric luminosity ratio Lx/Lbol by several orders of magnitude, which exists in these stars along with a significant spread in Li abundance. This may link the surface activity of stars with phenomena at the base of their convective zones. The TESS data allowed us to reveal rotation modulation of stellar brightness associated with starspots. For some twins of our samples, periods of axial rotation are detected around 6 days, i.e. these stars rotate almost 4 times faster than the contemporary Sun. This indicates their relative youth. Flare activity of solar twins is discovered in the TESS data; we showed existence of various kinds of flares, and present temporal profiles for some of them. We obtained the energy about of 8x10^33 erg for the largest flare of our samples, lasting longer than 4 hours. In addition, we discuss also magnetic fields and properties of exoplanets, orbiting these stars.