("Yes", with the proviso that the proposed silicon atom definition is a more obviously direct link than the watt balance.)
The Avogadro number isn't a fundamental physics constant, it's just a unit conversion constant, and thus, didn't get to define any basic unit.
That's a pretty arbitrary assertion. Who defines what "fundamental" is? The number of periods of <something> of Caesium atoms used to define the duration of one second doesn't sound very fundamental either.
Avogadro's number is used to define the atomic units, what makes a lot more sense than pushing it into metric calculations.
The wikipedia page is great:
What you want, is to go down to the smallest unit possible, which is apparently Planck's Constant.
Essentially, that's what they were doing with Le Grande K. It's unstable because molecular properties are unstable in aggregate.
You may be thinking "Oh, you fool--E=mc^2 is for fission and fusion, and certainly doesn't apply to things like the energy in the heat of an object". But weirdly, it does. https://physics.stackexchange.com/questions/87259/does-decre...
This typically only matters in a relativistic context, and doesn't impact day to day life. The difference in passage of time can be measured by an atomic clock if you put it on a rocket into space, but is otherwise insignificant. It's unlikely any scale could measure your weight-gain from climbing stairs, since the amount of energy you gain is insignificant when converted into mass. You can compute the mass gain by solving for "m" in the formula E=m*c^2, so m=E/(c^2).
The speed of light c is a really big number, and so to compute the mass you gain, you're dividing the energy by c^2, which is a much bigger number. Thus a gain to kinetic or potential energy does not noticeably affect your mass in day to day situations. Conversely, if you can convert any meaningful part of your mass into energy, then it's an absolutely tremendous amount of energy: atomic weapons.
I've never heard this before. Can you link to some further explanation? Intuitively, if anything, you'd lose mass, because you're in a place now where space is less curved than where you were before.
And yes, there's also some change due to changes in gravity. I'd expect that to be much smaller.
But IANAP, and not that good with relativity.
There is a very good reason for this approach. In the simplest, most classic way of deriving the special relativity from the first principles, the 4-velocity is introduced before the 4-momentum. I.e., γ and m are coming from different places and are not connected in any ways whatsoever.