I think most people think Sweden as our most natural ally. We may have a rivalry thing going on and make fun of each other all the time, but it's more like a sibling rivalry than any kind of real feud. Even though Sweden stayed neutral during WWII lots of Swedish men fought in Finland as volunteers. Even today our armies do practice battles together and collaborate on defense plans. Estonia is considered an ally too, but more like your cousin that's good for partying and holiday fun, but should never be relied on in a crisis.
Finnish is not really mutually intelligible with anything, though Estonian would be the closest in terms of vocabulary. If you speak Estonian you could ostensibly make sense of some Finnish, though this would be much like trying to read Japanese kanji with only working knowledge of traditional Chinese. There's also much room for misunderstanding, since there are some words that are used in both languages but with different meanings. For example, Estonian for "Where is the bathroom?" is "Kus on WC?", which in turn is Finnish for "Piss is the toilet". Likewise, "I have lost my bag" in Estonian is "Ma kaotasin oma koti", which a Finn would interpret as "I've misplaced my home". Hungarian, on the other hand, is almost completely different apart from some root words that maintain phonetic similarity. This also applies for Scandinavian languages such as Swedish, with the exception of a dialect speech near the Swedish border and slang speech in the capital region. The so-called "stading slangi", or "capital slang", is a weird mixture of mangled Swedish and Finnish. For example, here we have the sentence "Close the door so it won't blow in" first in (rough) Swedish, then Finnish and finally in slang.
Stäng dörren så att den inte kommer att blåsa in
Pane ovi kiinni ettei puhalla sisään
Pane döre kine ettei blosa ine
Note: This is an older example of slang. As language is constantly developing, I cannot guarantee you won't look like an idiot if you try this in 2014.