Heroes have a lot of symbols like the eclipse and the thing that niki and peter have if you know what i'm talking about. But who really know what they mean.
The weird curby thing is as said in first season a power of god but that thing could be the missing part of the DNA that you need to have powers. you know The DNA really looks like that symbols
The eclipse: No one really know how peter will get his ability or how to defeat Arthur Petrelli. I think that when there is an eclipse no one can use he's powers In the nexts episodes (I don't know which) but the title is eclipse part1 and the episode after eclipse part2. I think that during this episode no one will have his powers so then they can defeat Arthur.