Questions & Answers about Ég er þegar búinn með verkefnið.
Here þegar means already.
In this sentence, it shows that the assignment was finished before now, and that this is relevant at the present moment. Its position is also very natural: in a main clause, Icelandic often puts short adverbs like þegar after the finite verb, so Ég er þegar búinn ... is a normal word order.
Because vera búinn is a very common Icelandic way to talk about something that has been completed.
Literally, Ég er þegar búinn með verkefnið is closer to I am already finished with the assignment than to I have already finished the assignment. But in real usage, it often covers the same idea that English expresses with the present perfect.
So:
- Ég er þegar búinn með verkefnið = everyday, very natural
- Ég hef þegar lokið verkefninu = more formal/literary style
For learners, it is best to treat vera búinn as one of the most useful everyday patterns in Icelandic.