2. When Ukrainians (if the exist as a different nation) came to live in the are where is today Ukraine?
If you mean the central and western parts of the modern Ukraine, Ukrainians didn't come to live there from anywhere. They have always lived there. Ukrainians arose from ancient Russian people who fell under the rule of Poles, the Lithuanian and Austrian people. The very word "Ukraine" ("Украина" in Russian) is a dialectic variant of the Russian word "окраина" (or maybe its Polish equivalent), which means "outskirts", "outlying districts". So, the word "Ukrainians" actually meant the people living on the outskirts of the country. The modern use of this word denoting ethnicity arose somewhere in the end of the XIX century. Before that such words as "Малороссия" (Small Russia) and "Малорос" were usually used to denote the territory of the central part of the modern Ukraine and people who lived there.
The eastern and south parts of the modern Ukraine were scarcely inhabited until they were joined to Russian Empire in the XVII and XVIII centuries. Then these territories were populated with immigrants from the central parts of Russia, from the central and western parts of the territory of modern Ukraine and from the Don's Cossaks' territory. So the population of these territories is very mixed - you can find here people speaking Russian, Ukrainian or a mixture of the languages, called in Russian "суржик".
The historical study of ancient Russian language shows that the detachment of the Ukrainian dialect from the ancient Russian happened somewhere in the XIV century. Before that time there is probably no sense to speak about Ukrainians as a self-dependent nation.