The piano fits for Sakamoto over a sword or a dam because he is a musician who spent his life with the piano as his primary instrument. It's where he is most experienced and he has a much closer relationship to that than a dam or a sword.
Ivory is also typically only used for the keys, and doesn't actually impact the tuning of the instrument.
He was also referencing a specific piano, an old Yamaha piano in the gymnasium of Miyagi Agricultural High School, which had been damaged by the tsunami. It seems very unlikely that a high school Yamaha grand piano had ivory keys.
What surprises me is that the description seems to imply a wooden framed piano.
They exist, but they are notoriously difficult to tune and keep in tune compared to iron framed pianos. I think they have stopped making them for quite a while. I find it hard to imagine a high school using an instrument requiring so much maintenance.
If it was indeed a wooden framed piano, it was probably more of an antique than a practical instrument, and so, maybe with ivory keys, though again I doubt it.
They used to, but once cast iron frames could be made that's how it was done, initially in several pieces, and later in one piece. The story of how this came to pass is quite interesting, making such large casts isn't simple.
Yes, in fact that's how it started. The 'upright' was a way to sell pianos to lower income families because it's cheaper to manufacture and easier to situate in a small home. Prior to 1825 all pianos were made of just wood, and played reasonably soft, usually with just one or at most two strings per note (that's where the term Una Corda originally comes from, now it denotes a pedal that (on grand pianos) causes the action to shift a bit to the right so it will miss a string in the higher register).
That also made them pretty finicky, changing moisture and temperature would have a significant effect on the pitch of the piano. At that time 'standard pitch' was about A4@423 Hz, considerably below what it is today (A4@440), which lessened the problems somewhat but if you wanted to have your instrument well tuned you had better learn how to tune it yourself.
For harpsichord players (the predecessor to the piano) today self tuning is still the standard.
Piano history is fascinating, if you are interested in the subject I'd recommend reading 'Of men, women and pianos' by Arthur Loesser. It's an old book but a fantastic source of historical information about the development of the piano/grand piano.
Ivory is also typically only used for the keys, and doesn't actually impact the tuning of the instrument.