The particle will appear to live longer only to the outside, "from the point of view of the particle" the lifetime isn't altered.
That's what I was talking about.
No, it's still a minute to us. Speed and time are all relative to the observer.
That really not what relativity says.

If that was so then the experiment where they flew an atomic clock around the Earth at high speed wouldn't have worked, would it? We would still have observed the atomic material decaying at the same rate (from the ground, not on the plane). But it didn't, it lasted slightly longer.