CONCLUSION:
The initial surface is infinite and that is a cause of considered bug.

1. Operations with initial cases.
   
   1. intersect command.
      The intersect command produce nothing.
      
      
   2. extrema command.
      The result of extrema command is unpredictable for current case.
   3. BRepIntCS command.
      BRepIntCS produce correct result.
      
      
2. Operations with trimmed surface.
   If we use trim command the results of operations are better.
   
   trimv st s -80 0
   
   1. intersect command.
      The intersect command produce valid result.
      
      
   2. extrema command.
      The result of extrema command is not full. We have only one extrema, but we shoult have two.
      
      
   3. BRepIntCS command.
      BRepIntCS produce correct result too.
      
      

CONCLUSION:
The initial surface is infinite and that is a cause of considered bug.