Learn Swedish: Hunden är trött och vilar i sängen. - The dog is tired and rests in the bed.

Because the dog is actively resting right now. Vilar is the present tense ("rests" or "is resting"). You would use the infinitive base form vila (often with the marker att) if another verb came first. For example, to say "The dog likes to rest", you would use the infinitive: Hunden gillar att vila.

Why doesn't the sentence say "och är vilar" for "and is resting"?

Swedish doesn't use "is" (är) to show that an action is happening right now. The present tense verb vilar translates to both "rests" and "is resting" all on its own. Adding är before an action verb is a common trap for English speakers!

Why do both hunden and sängen end in -en?

In Swedish, the word for "the" is usually attached to the end of the noun as a suffix. Hund means "dog" and säng means "bed". Since they are both "en-words", adding -en to the end makes them definite: "the dog" (hunden) and "the bed" (sängen).

Would the word trött (tired) change if there were two dogs?