Sorry to dissapoint you, Cerjak, but that helmet is most definetely a tourist item and likely of a fairly recent manufacture (late 20th century). The telltale signs are a non-sliding (welded) nasal and the "horns" - not a very practical feature to carry on your head in battle
Your axe on the other hand, looks like a good period example (mid to late 19th century). While it mostly resembles a parade weapon, it's less lavish than usual decoration makes me believe that it could have more functionality than just a display item. The haft is not likely to be a made out of a barrel. These Persian axes are known for having hollow metal hafts almost exclusively. The lack of any finale at the botom makes me think that it was designed to conseal a stiletto, which appears to be missing now. Seeing any internal threading at the end of the haft would verify that.
Overall I think it is a lovely axe that would compliment any collection of Indo Persan arms.