Questions about Brokos' Play Optimal Poker

I originally posted this in Beginners' Questions, but I was advised to post here:

Hi guys, new poker player here, I'm currently reading Play Optimal Poker to get a grasp on the fundamentals, and I have a couple of questions. I hope someone here can help me.

First question:

In the chapter Reciprocal Ranges, Half-Street Game, Question 5, the answer says that betting 1/2 pot is +EV for Ivan, but a bet size of 1 pot makes the game 0 EV. So, not betting at all is 0, betting pot is 0 too, and in between there's a +EV bet size. It doesn't say so in the book, but that clearly means that there has to be an optimal bet size for maximum EV.

I worked out that given a value hand percentage v (in the example v = 1/2, meaning half of the hands in Opal's range are value hands she will always call with, the rest are bluff catchers that are indifferent), the bet size (as a fraction of the pot) at which the game reaches 0 EV is 1/v - 1, and the optimal bet size for maximum EV is 1/sqrt(v) - 1.

For instance, in the book example with 1/2 of Opal's range being +EV calls, that means that betting pot makes the game 0 EV, and betting about 0.41 pot is optimal. If 1/3 of Opal's range are +EV calls, a bet size of 2x pot makes the game 0 EV, and betting about 0.73 pot is optimal. If 2/3 of Opal's range are +EV calls, a bet size of 1/2 pot makes the game 0 EV, and betting about 0.22 pot is optimal.

So, long story short, this makes sense to me in the toy game, but what I'd like to know is whether and how this concept of optimal bet sizes is applicable to actual poker, what are the necessary adaptions, and what's the best book to read up on this?

Second question:

In the chapter Reciprocal Ranges, Full Street Game, Question 3, the answer says that "not coincidentally, the frequency with which Ivan calls with a K is exactly the same as the frequency with which he bluffs a Q". The way I understand this, though, it actually is total coincidence.

Crunching the numbers, I'm coming up with (-bv) / (b - bv - v + 1) for Ivan's frequency to call with a bluff catcher (b being the bet size as a fraction of the pot, and v being the percentage of +EV calls in his range). For Ivan's frequency to bluff, I'm coming with (bv + v - 1) / (b - bv - v + 1). Those two are equal only if v = 1 / (2b + 1), or formulated differently, v = 1 - 2PO (PO being the pot odds the caller gets). Another way to say this would be this: For the frequencies to be equal, the bet size has to be exactly half of the bet size that makes the game 0 EV (see previous question; this is not the optimal bet size).

So, this clearly works out in the book example with v and b both being 1/2. As soon as the bet size changes, though, particularly when choosing the optimal bet size, it seems those frequencies aren't equal anymore.

My question is, am I totally off here or is this an error in the book? Not sure what to make of this, please tell me where I'm wrong.