Translation:The boy rests.
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Your last option should be "Jeg trænger til at hvile."
The words to and at are called infinitive particles (infinitivpartikel/infinitivpartikler) or infinitivemarkers (infinitivmærke/infinitivmærker)
Det var så lidt!
Forresten: Tak skal du have.
de means they – du means you (sg.)
Most languages have a formal and an informal word for you and we have it same in Danish with 'De' (formal) and 'Du' (informal). However we really don't use the formal one today. The only examples I can give are when talking directly to very old people or to one of the members of the royal family. http://programmer.tv2.dk/tillykke-margrethe/2015-04-13-dronning-margrethe-afbryder-journalist-vi-er-ikke-dus