Intentional. Only the most common contractions (it's, we're etc.) are accepted. Making the contracted 's correct in all places would require too much work of us contributors.
Oh. I'd have hoped at least "who's, what's, where's, when's, why's & how's" would have been added. Oh well!
Can we form the opposite adjective in most cases just by adding the prefix "o-" (like "un-" or "il-" in English)?
"Omöjligt" is an adjective, not a noun. But yes, o- is basically equivalent to the English un- and its variations.
I translated it in "Why is it not possible", which may sound a bit rare, but I don't think it should be judged as incorrect.