Language barriers in Ukraine

Well, Ukrainian IS the only official language of Ukraine, but it's amazing how few people speak it outside the far west. It is more patriotic to learn Ukrainian, and it's definitely a language more pleasing to the ear than Russian. (Mila Kunis, from Chernivtsi originally, described Russian as like "listening to Klingon") Ukrainian is the 2nd most musical language in the world, after Italian. More and more people are learning Ukrainian, who only spoke Russian before, I speak both.
In answer to your question, yes, you will definitely need to learn either Russian or Ukrainian, and when you take into account that Russia is the enemy, and invaded Crimea and Donbass, I recommend that you learn Ukrainian.

The farther west you go in Ukraine, the more prominent Ukrainian language is.  I have been to the Donbass region before the war, which is the complete opposite end of Lviv region, and nearly nobody speaks Ukrainian.  Though Ukrainian is a very beautiful language to learn, Russian is far more practical.

Yes, but if you don't care about Ukraine, then speak Russian. But personally if I meet some gold-digger from Donbass who doesn't want to learn Ukrainian, I tell them to get lost!!! (or F*** O** back to Russia!)