Learn Dutch: Ondanks dat de kou extreem is, overleven we. - Even though the cold is extreme, we survive.

No, you need dat here. Ondanks is a preposition used directly with a noun or noun phrase (like ondanks de kou - "despite the cold"). Because you are introducing a full clause with its own subject and verb (de kou extreem is), you must use the conjunction ondanks dat ("despite the fact that" or "even though").

Why is the verb is placed at the very end of the first part before the comma?

The phrase ondanks dat is a subordinating conjunction. This means it introduces a dependent clause (a sub-clause), which forces the conjugated verb (is) to move to the end of that specific clause.

Why does the second half of the sentence say overleven we instead of we overleven?

The entire first clause (Ondanks dat de kou extreem is) acts as the first block of information in the main sentence. Since Dutch requires the main verb to be in the second position (the V2 rule), the verb overleven must come right after the comma. This pushes the subject (we) behind the verb, which is known as inversion.

Why is it de kou and not de koud?