Learn Italian: Un miliardario non lavorerebbe ogni giorno. - A billionaire would not work every day.

It is the present conditional for the he/she form. For regular -are verbs like lavorare, you drop the final -e, change the characteristic -a- to an -e-, and add the conditional ending -ebbe. This gives us lavorerebbe (he/she would work).

Why do we use the conditional lavorerebbe here instead of the normal present tense?

We use the conditional to talk about hypothetical or imaginary situations. Saying non lavora would mean a specific billionaire literally does not work. Saying non lavorerebbe means a billionaire generally would not work in this imaginary scenario.

Could I say tutti i giorni instead of ogni giorno?

Yes, both mean 'every day' and are completely interchangeable here. Just remember the grammar rule: ogni is always followed by a singular noun without an article (ogni giorno), whereas tutti requires the plural article and noun (tutti i giorni).

Is miliardario a millionaire or a billionaire?