"The child likes to jump high."

Translation: Barnet tycker om att hoppa högt.

[takver]

What is causing 'hög' to be declined as neuter here? Are all adverbs automatically declined as neuter?

[Zmrzlina]

Yes, adverbs are formed as a neuter adjective.

[dave527603]

Can you "gillar" on verbs like jumping?

[Arnauti]

Sure, barnet gillar att hoppa högt works just as well.