Some nouns in English can also be used as adverbs. I might call this the locative case of downtown. You'd say "The bank is far" not "The bank is in far", because far is an adverb. I guess you'd have the same flexibility as downtown when using either: "The bank is south" or "The bank is in the south". Another noun that seems to have a locative case would be home in "We are home" rather than "We are at home" or "We are in a home". This only works with special words, like downtown.
Nah, it's not a good translation. Centrum is a noun, not an adverb. Although, it can be used to mean center of something, rather than downtown.
Also, I found an interesting entry that said ""Swedish uses centrum for the shops at the centre of a suburb (Farsta) or small and medium-sized town (Uppsala), while the centre of a larger city (Stockholm) is often called city.""
We use is in multiple ways in English but är is not used for all of them. For "It is [located] there" or "It is [situated] there", ligger is used. You could even say it that way in English: "The town lies in the valley". I like to think of it like someone laying a tile with a picture of a bank onto a map.