"The crown princess is in town."
Translation:Kronprinsessan är i staden.
This is one of the cases where English prefers to use the indefinite. It's of course possible to say in the town, but in town is probably the default version. In Swedish, we don't do this. Since it is known to both the speaker and the listener what town we're talking about, we say staden (or colloquially, stan).
The reason you can say in town in English even though you're speaking about a specific, known town, is probably that 'in town' has come to be perceived as a kind of unit.
Is i stan a direct translation to in town? It is weird because no other Germanic languages have a direct translation to my knowledge.
You might also find "stad" being used as "place" in some words in Swedish, like "fristad" ("safe haven, sanctuary") and eldstad ("fireplace").
That's good to know. There are a couple dozen words in English ending in -stead, too. The only one I've used myself is farmstead, but a few like bedstead (where a mattress goes) are still in common use. Most, like gravestead or playstead, have a much more common word (e.g. graveyard, playground) and are so rare people would look at you funny if you used them. Many others are basically lost to history, like mowstead (a place to store stacks of mowed hay or corn/grain).
Steady and steadfast have an etymological connection, too.
But I think I'll start using firestead. It's not in the dictionary, but I like it.