Whether the Slovaks already existed as a separate nation? How can you be sure?

However, Slovak nation as such, has existed always, just never had nation state of their own. First state created out of independent Slavic tribes which included Slovaks was Moravian Empire, then came Hungarian Empire, then came Hapsburg Empire, then came Austro-Hungarian Empire, then came Czechoslovakia and then only much later did Slovaks have own state.

Greater Moravia came into existence by joining of Moravian and Nitrian principalities. So there was Principality of Nitra with Prince Pribina before it.  (for orientation wiki  http://en.wikipedia.org/wiki/Principality_of_Nitra )

Principality of Moravia – today's Moravia
Principality of Nitra – today's Slovakia
the core of Greater Moravia

Nitrian Principality started to exist in 8th century and definitely extincted in 12th cent. (because of centralization of Regnum Marianum – later Kingdom of Hungary).