Is the constitution a rebublican document?
Yes, if you mean republican with the little "R". The USA is a republic, not a democracy.
Of course the statement "the constitution is a living document" is metaphorical, since no document is living, it's a piece of paper with writing on it. As a metaphor, this statement would suggest that the constitution remains relevant and connected to the society which it helped to establish in the late 18th century, which is a long time ago. If you think that the constitution has become irrelevant, then you would say that the constitution…
The United States Constitution was the document that established the Federal system of government. The US Constitution was, in its time, a revolutionary document that recognized the freedoms of its citizens. At the time of its ratification, most of the world's established countries did not have the freedoms the the US Constitution recognized.
The UK has an unwritten Constitution. Its laws are not codified into a single document. The UK does have a constitution, the difference between the USA constitution and the UK one is that fact that in the UK there is an uncodified constitution. (means it is not written down in one single document, but is formed through laws and legal precedents).