Learn Swedish: Polisen kan ha följt fotspåret längs vägen. - The police may have followed the footprint along the road.

When you combine kan with ha and a supine verb (like följt), it expresses a possibility about a past event. We use it to deduce what might have or may have happened, rather than talking about someone's literal physical ability to do something.

Could I use kunde ha följt instead of kan ha följt?

You could, but it changes the meaning! Kan ha följt means "may have followed" (we do not know if they did or not). Kunde ha följt means "could have followed"—which usually implies they had the opportunity to do it, but we know they actually did not. For deducing what actually happened, stick to kan ha.

Why is Polisen singular when English treats "the police" as a plural?

In Swedish, polisen is a singular noun referring to the police force as a single institution. English says "the police are", but Swedish effectively says "the police force is". If you want to talk about multiple individual officers, you would use the plural poliserna.

Is there a rule for using the definite form vägen after längs?