Learn Icelandic: Venjulega vaknar hún heima. - Usually she wakes up at home.

This is the V2 (verb-second) rule in action! In Icelandic, the verb almost always takes the second spot in a main sentence. Because we started with the adverb venjulega (usually), the verb vaknar must come next, pushing the subject hún (she) into the third spot.

Can I say Hún vaknar venjulega heima instead?

Yes, absolutely. Starting with hún follows the standard subject-verb order, and the verb is still in the second position. Moving venjulega to the front of the sentence, like in this example, just puts a little more emphasis on the fact that this is what usually happens.

Why is the word for "at home" heima and not heim?

Icelandic has different words for location (being somewhere) versus destination (going somewhere). Heima means being "at home", which fits perfectly here since she is just waking up there. You would use heim if there were movement towards the house, like going or walking home.

Is venjulega related to the adjective venjulegur?

Yes! Venjulegur means "usual" or "normal". Changing the ending to -a is a very common way to turn an adjective into an adverb in Icelandic, exactly like adding "-ly" in English to turn "usual" into "usually".