Indeed it is.
No, that's a different subject. This is limited to the effect on (of?) interest rates on the value of debt. Interest rates also affect the value of currencies. But the value of currencies is a separate discussion and that one of the places where Baldee gets confused.
The principal isn't affected by anything. It's fixed at the time of purchase and it doesn't change. The principal amount is always the same. Today a debt may trade a par, tomorrow it may not. The value of the currency (i.e. purchasing power) may change over time. But the value of the debt, independent of currency valuations, will change as interest rates change.
If you are not talking about currency, then I think you missed his point of view.
He is being very clear that a debt has two components, the unpaid principal amount which remains unchanged and interest amount which keeps varying as the rates change.
I think your reference about debt trading at par or below or at premium is direct adjustment of interest rates (IR) with inflation (I). Consider IR > I or IR = I or IR < I. I would love to borrow if IR < I.