I heard that Russian and Ukraine are similar, along with Swedish and Norwegian. If I learn one, will I pick up on the other more quickly?
Yes. Russian and Ukrainian aren't super close, but they are close enough that if you knew one, then you would have a huge advantage with learning the other. The same goes for Swedish and Norwegian. It will still take work, but not as much if you know one and learn the other. I hope this helped!
Absolutely. I am given to understand that Swedish and Norwegian are very close indeed, to the extent that Norwegians and Swedes actually speak their own languages to each other as opposed to using English (which they tend to do with Danes, whose language is also referred to as mutually intelligible).
Native Russians I've met have said they can understand about half of Ukrainian. Having done the Ukrainian tree as a fairly advanced learner of Russian, it was very straightforward. Very frequently I wouldn't have needed to use the hints even for new words.