Usage of twice and two times with "size"

The reason you can't use "twice bigger than" is simply because this is a phrase we do not use. I am not sure exactly why, maybe someone else has a better reason than that, but I do not. The information presented by your grammar book is just about the grammatical correctness of each substitution, as opposed to making a sentence with a similar unambiguous meaning.

For the other pages you have linked, the question isn't of grammar, but in exactness and level of ambiguity.

Referring to your last question about "two times loner than ... " vs. "two times as long ..." This will confuse native speakers too. They are saying that the difference in the usage is that in the first, "two times" describes how much longer and in the second, "two times" describes the actual length.

I tend to disagree, and think that the first usage is ambiguous enough for most people that it shouldn't really be used.

As other posters in the answers you have linked point out (and is reinforced by the difference in answers), using "times more than" form is pretty ambiguous, or difficult to ensure your meaning is accurately understood.
if X and Y are numbers

"Y is two times as big as X" --> Y is 2*X (Y: 4, X: 2)

"Y is 200% of X" --> Y is 2*X (Y: 4, X: 2)

"X has increased by 200% to become Y" --> Y is X+2*X (Y: 6, X: 2)

"Y is two times bigger than X" could be referring to both of the situations above (Y being 4 or Y being 6.) Some may argue one way or the other, but the fact that it is unclear is definitely apparent.

When there are two expressions that logically mean the same thing, but only one of them is used, this simply means that one expression has gained currency, and the other one has not. In the case of twice as big as/bigger than, there's no logical reason that one dominates over the other, but a quick look at a usage graph shows that as big as is pretty much used to the exclusion of bigger than after twice.

Google Ngram

The practical reason for using the preferred form over the unpreferred one is simply not to look like an outsider or to appear not to have a strong grasp on colloquial English. In simple terms, you want to sound normal.

In any case, I'd recommend the as (adjective) as in all cases, even when the other version is allowed, as it seems to me to impart greater clarity.