These 2 quest are said to be the most important one, concerning the decision of your (potential) future allies (and enemies). It is common knowledge, that the side you pick at Gold Rush, will prohibit you from joining the opposite one during Free Elves. But...

In the Witcher wiki site, under the entry of "siegfried of denesle", near the bottom of the page, says this: "During the Gold Rush quest, if Geralt sides with Siegfried and the Order, the soldiers will help him later in the Salamandra hideout, and at the end of Chapter IV, he can still choose to either remain neutral or side with the Scoia'tael. ". Is it true that siding with the order makes it possible to choose from all 3 different possibilities, during the Free Elves quest? And if yes, how? Again, some official info or proved to be true, would be greatly appreciated.

The page is simply wrong. If you side with the Order in 'Gold Rush', you cannot side with the Scoia'tael during 'Free Elves'. 'Free Elves' gives you the option of siding with your choice in 'Gold Rush' or escaping while the Order and Scoia'tael slaughter each other: there are never more than two options when Dandelion asks you what you're going to do, and the non-neutral option is always linked to your choice in 'Gold Rush'.

It's worth noting, of course, that the page on Gold Rush directly contradicts the snippet you quoted: "Please be careful with your choice, since your choice in this quest will have a significant plot impact on Chapter IV's Free Elves quest. Once you have chosen to fight against a particular side in this quest, you can no longer support that side in Chapter IV. You can not change your mind. (So, as they say in one movie about shining cups, choose wisely.)"

The page on Free Elves also contradicts it: "your choice in Chapter III's Gold Rush will actually limit your choice in this quest."