Learn Swedish: Hon betalar, men var är kortet? - She is paying, but where is the card?

In Swedish, there is no separate continuous tense (like 'is doing'). The present tense betalar means both 'pays' and 'is paying'. Saying hon är betalar is a common beginner mistake, but it is incorrect!

How do we know kortet means 'the card'?

Kort is an 'ett' word (ett kort = a card). To make an 'ett' word mean 'the', Swedish adds the definite ending -et to the end of the word, making it kortet.

How would I change this sentence to say 'where is THIS card?' using what we learned in this lesson?

You would say var är det här kortet?. Because kort is an 'ett' word, you use det här instead of den här. Also notice that in Swedish, when you use det här or den här, the noun that follows must stay in its definite form (kortet).

Why do we use var for 'where' here instead of vart?

Var is used when asking about a fixed location, like finding where a lost card is. Vart is used when asking about direction or a destination (like 'where are you going?'). Since the card is not moving somewhere, var is the right choice.