Learn Swedish: Var är vi? Rutten korsar en flod här. - Where are we? The route crosses a river here.

Var means 'where at' (position), while vart means 'where to' (direction). Since the speaker is asking about their current static location (Var är vi?) and not their destination, var is the correct choice.

Why is the word här used instead of hit at the end of the sentence?

Just like var and vart, Swedish distinguishes between här (here, position) and hit (to here, direction). Because the route crossing the river describes a geographic feature at a specific location rather than a movement towards a destination, we use the positional här.

The word for 'the route' is rutten, but doesn't that also mean 'rotten'?

Yes, it does! Rutten can be the definite form of the noun en rutt (the route), or the adjective rutten (rotten). You can easily tell them apart by context here, as saying 'the rotten crosses a river' makes no sense.

Is there a difference between en flod and other words for river like en älv?