Is 'redemption yield' just another term for 'Yield to Maturity'
Yes. It is the yield you will earn if you hold the bond until it matures (any change in market price after you buy it is irrelevant).
Is 'Interest yield' just the same thing as 'Yield rate'?
Yes (I have also heard this called "coupon yield"). Interest yield is the amount if interest you get ...
There are famous proofs by Arrow & Debreu and others, based on the Kakutani Fixed Point Theorem, but they are at a very abstract and general level. I am not sure the details of market mechanism matter, as long as excess demand affects prices, and prices affect excess demand, there will be a convergence to a price equilibrium.
There is no mathematical proof of EMH. You would need all market participants to agree on a singular pricing model for that to be possible. Without a singular, agreed-upon model, what you are asking for is proof that people's collective opinions represent people's collective opinions. This is called a tautology.
There is an endless number of ...
In a nutshell, this is the "variance drag" problem. The mechanics of how you short something matter, and it's relevant to the discussion of levered/inverse ETFs that behave differently from classic/vanilla positions.
Consider an XYZ future at 100. A day later it's 1% up, at 101. Two days later, it's up 1% again, at 102.1.
If I go long, I make 2.1 profit. ...