No you are wrong - The word 'decade' is not tied to any specific set of 10 years, so you can mark off any set of 10 years and call it a decade: 2000-2009, or 2005-2014, for example. By your logic the year 2000 should be part of the 90's which it wasn't.

Yes wrong. The first decade was either 9 or 10 years (depending on whether you want to be weird and include 1 BC), every decade after that was 10 years starting at 'X0 and ending at 'X9. This is how the common usage defines the term.

A lot of concepts in daily human lives get fuzzy near the edges. That's not a failing on humans, that's how language works. This isn't scientific or perfectly rational, yes, but neither are humans.