A couple of points.
The toy games are static. The relative values of the hands don't change. Real poker games are dynamic and relative values may change from street to street.
In a three street game calling 1/2 of the time means you can only call all three bets 1/8 of the time.
Still haven't seen any papers on how additional cards affect strategy.
In real poker on the turn if it costs 1/4 or more of your stack to call, the correct options may be fold or go all in. If the guy has it, it'll costs all your chips to see his hand. You may as well go all in now and not give him a free draw.

No, look at this quote from page 7. On the river opponent bets the pot.
You should always fold if he's not likely to be bluffing one time in three.
High enough isn't very high.
On the turn you should always fold unless he's bluffing at least 5/9
of the time. Very few players are bluffing that often. I think these
results are saying always fold to a big turn bet, unless you know
this player bluffs a lot.

P0, the 0 is suppose to be a subscript. 2+2 doesn't support subscripts.

Yes, if my opponent might fold a better hand to my all in or call a worse hand. But if my opponent's range is polarized, it's more like the toy game (Clare knows. She is either bluffing or has a monster). If that situation exists (or approximately so) then calling P/(P+B) on all rounds is better than going all in.

Going all in when opponent is either bluffing or has monster:
[1] if opponent is bluffing I gain nothing by going all in over calling 50% on each round. Same EV either way.
[2] if opponent has monster I lose my remaining stack S close to 100% of the time (depending on my chance of outdrawing). Calling P/(P+B) on each round, I lose (1/4)S(1/2) + (3/4)S(1/4) = 7/16S.

But in the real world, there are gains to going all in when opponent holds a medium-good hand.
[1] He may call a hand that's better than mine, but I may outdraw him.
[2] He may fold a hand that's somewhat better than mine.
[3] He may call a hand that's somewhat worse than mine.

Those gains have to outweigh the losses I incur above when he holds a monster.

If the toy game points to ~50% calling it does so when there is a lowish chance of outdrawing and when opponent's range is likely to be polarized.

There's a fourth.
[4] He may be betting a semi-bluff with a drawing hand.
Let him draw for all the chips.

Also this strategy applies only for when you're calling for over 1/4 of your remaining stack.

True but when I said the toy game points to possibly ~50% calling as defense of bluffs, I was picturing non-drawing situations, not semi-bluffs.

Something like, I raise preflop wtih AA, get one caller, flop comes J72 rainbow. I raise, he reraises enough to make me pay P into a pot of P. I think I should be calling something ~50% of the time on each betting round.

Pushing that up somewhat are the facts that
[1] I do have a few outs if I call, esp. if he has only two pair
[2] He could have KK or QQ in which case folding 50% is a big mistake.

Pushing that down slightly is that fact that I don't really need to call 50% of the time with just AA (no set) to make him indifferent to bluffing since sometimes I'll hit a set myself and never fold.

Not recommending fold or push with deep stacks. Only think it's best when the call would cost a large amount of my chips.
With three streets it costs 13 pots to call three times.
1 for 1st st.
3 for 2nd st.
9 for 3rd st.
In a cash game you open for 3 X BB. One player calls. With three streets of betting, it costs about 90 to 95 BBs to play this hand. That's nearly your entire buy-in.
After the flop opponents donk bets. I'm not risking 90 chips to protect 3 chips.

Wow. i've never tried this kind of game before. I did play some complicated games from top1apk, however, this one seems more complex. I'm not good at maths. Actually, i'm quite bad. So, anyone can tell me how to understand it in the easiest way?

Someone sort of stumbled into MDF and bluff ratios by himself. Yeah I was freaking out the first time I started to study all of this too. Yes, with clairvoyance (or just the nuts) you can win much more than its in the pot, and the math for calculating that in idealized spots is easy. You guys should read matt Janda's applications where he goes trough all of this.
Btw, I'm on study group where we discuss theory like this regularly. Anyone here wants to join? Just pm and I'll send the invite link