If I say, ' The soup is a popularly traditional dish in the country,' is the use of adverb, 'popularly' instead of ' popular,' wrong?
Yes, that is wrong. You are speaking about a traditional dish that is popular, so it is a popular traditional dish. "Traditional dish" is a lexical unit.
I know the phrase, 'in such a relatively short period' sounds right,
but can I say like this?
How can they establish the building in relatively such a short period?
Although some occurrences of "in relatively such a short period" can be found on the Internet, I'd definitely use "in such a relatively short period," which is much more usual and where the adverb relatively modifies the adjective short. In the other phrase, the adverb relatively seems to modify such a short (i.e. so short), and it does not sound quite right to me for relatively to modify an intensifier. We would never say, for example, that something is relatively very short. It can be relatively short, not relatively very much so.