Learn Arabic (Modern Standard): ارتفع دخل العائلة هذا العام.

Form VIII verbs often take on a reflexive or middle meaning. While the Form I verb رفع is transitive and means to raise or to lift something, the Form VIII ارتفع is intransitive and means to rise or to go up by itself.

Why isn't there a preposition like في before هذا العام to say 'in this year'?

In Arabic, expressions of time can function directly as adverbs of time (zarf zamaan) without needing a preposition. When used this way, the phrase is grammatically in the accusative case (mansub) and naturally translates to 'this year' or 'during this year'.

Is there a reason to use العام instead of السنة for 'year' in this sentence?

Both words mean 'year' and are largely interchangeable. However, عام is typically used for a solar or financial year, making it a natural fit for an increase in income. Note that عام is masculine, which is why it uses هذا, whereas سنة is feminine and would require هذه.

Does the Alif at the beginning of ارتفع have a regular hamza or a hamzat wasl (connecting alif)?

It is a hamzat wasl. The past tense of Form VIII verbs always begins with a connecting alif. Because it is the first word in the sentence, you pronounce it with an 'i' sound ('irtafa'a'), but if it came after another word, the 'i' sound would be dropped and you would connect the pronunciation directly to the 'r' sound.