Learn Portuguese (Portugal): Quem paga o prejuízo da humidade é o seguro. - The one who pays for the damage from the damp is the insurance.

Starting with Quem is a very natural and concise way to say 'The one who', 'He who', or 'Whoever'. It acts as a pronoun that already includes the idea of 'the person'. You will hear this structure often in spoken Portuguese to emphasize who is responsible for the action.

Does prejuízo mean the physical damage to the house?

It leans more towards the financial loss or cost of the damage. For physical damage, you would more commonly use the word dano. Since the sentence talks about paying, prejuízo is the perfect word to describe the financial burden caused by the situation.

I learned humidade as 'humidity' in the weather. What does it mean in this context?

In a household context in Portugal, humidade specifically refers to 'damp', including water spots, mold, or condensation issues on walls and ceilings. It is a very common housing issue to discuss.

Since this lesson focuses on the resultative passive (ficar + past participle), how would I say 'The house was damaged by the damp'?

You would say A casa ficou danificada pela humidade. Using ficar (to stay/become) with the past participle danificada is perfect here because it emphasizes the resulting state of the house after the damp affected it, rather than the action itself.