Three S. N. Chernikov's questions

The author shows: the class of all periodic non-locally finite and non-locally nilpotent $FNN$-groups is non-empty and wide; an arbitrary binary graded $\overline{IH}$-group is solvable. At the same time, the author solves three natural S. N. Chernikov's questions. Also the author establishes that a non-Chernikov non-abelian group with normal such subgroups is solvable iff it is binary graded.