How does the Spanish Tax Agency view US S-Corporation income?

1. Would the S-Corp's total annual income need to be declared as personal income in Spain?

No, in theory not. Spain respects corporate income as such, so corporate personal income uses a different personal tax (IS) than personal income tax for natural person (IRPF).

2. Would the ~240K USD that remained in the S-Corp be taxed at a US corporate tax rate?

Yes, exactly. That money isn't in Spain, and arguably isn't generated in Spain; Spanish tax authorities have no business about it.

3. Is only the invoiced income (the 50K EUR) considered personal income from the perspective of the Spanish Tax Agency? Or is the S-Corp's total income included?

Depends. If they open inspección on you (God knows) and they (most unfortunately!) come to the conclusion that you simulaste (cheated), they would sum the company income to your personal income tax. And, hopefully, they would inspeccionar your company too at the same time, in order to remove that income from the company IRNR in case they considered the income corresponds in your personal income tax. Otherwise, the answers here are yes (1st) and no (2nd question). But scenarios can be depending on whether how exactly the company operates in Spain, if at all.

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That'd be the general rule for all citizens from most countries, but I thought US citizens are an exception that always were to be taxed by USA...

S-Corp might operate in Spain through an establecimiento permanente, that is, an W entity (for "wholly owned"), I'm guessing it doesn't do, in your example. If it does, consider that tax inspection competence on that subsidiary is obviously Spanish!

You should procure professional advice.