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.
Daily usage differs from that definition of course, but that's not the point.