Yes, we need preceding utterance-contexts or situational contexts to make or interpret the omissions above.Do you mean that an expression such as "Amerika wa Nihon no nibai da" would be understood in Japanese even as is? Or is there preceding context that makes it clear that we are talking about population sizes and not something else? Or does the speaker just have to guess?
Finnish is pro-drop and allows for more possible omissions than English, but it's still not like Japanese, since we don't have the grammatical means to indicate the topic in a sentence; it is often placed first in the sentence, and the word order is flexible, so you can topicalize most constituents in a sentence. So in a restaurant, you could say something like Minulle ankeriasta (= "to-me eel") when the waiter wants to know what you'll be having, i.e. the verb can be omitted in this case. But you couldn't reply (Minä) olen ankerias to the waiter as it would mean you are an eel.
Also, Finnish is not Ural-Altaic and definitely not a sister language of Japanese. The Ural-Altaic hypothesis is long obsolete. Granted, there are some typological similarities in many of the languages of central and eastern Eurasia, but nothing points to a common origin.
Thank you.I'm not sure if this is related to the discussion, but in Finnish you can also say, for example, "Luen (Agatha) Christieta", which is "I read Christie" in English meaning that "I read a book by Agatha Christie".