Questions & Answers about Ja, jag tvättar bilen.
If this is the answer, how would you ask "Are you washing the car?" in Swedish?
To ask a yes/no question in Swedish, you put the verb first. So you swap the subject (du) and the verb (tvättar) to make the question: Tvättar du bilen?
Why does "jag tvättar" translate to "I am washing"? Is there a word for "am" missing?
Swedish does not have an "am doing" form. The single present tense verb tvättar translates to both "wash" and "am washing" in English. You just use the one verb!
The dictionary says the word for car is "bil". How does it become "bilen" here?
Swedish creates the word "the" by adding an ending directly to the noun, rather than using a separate word before it. Since bil is an "en" word (en bil), you add the -en ending to it to make bilen (the car).
Why don't we use the verb-first order for this sentence?
Because this sentence is a statement, not a question! You use the verb-first order to ask a question like Tvättar jag bilen? (Am I washing the car?). But to state a fact or answer a question, the subject comes first: jag tvättar (I am washing).