Learn Italian: Cammino ogni giorno e sono in forma. - I walk every day and I am in shape.

The word ogni translates to "every" or "each" and must always be followed by a singular noun. If you wanted to use a plural, you would use the phrase tutti i giorni (literally "all the days"), which means the exact same thing.

Could I say io cammino and io sono in this sentence?

You could, but it sounds slightly unnatural. In Italian, the verb endings for cammino and sono already make it perfectly clear that the subject is "I". You generally only add the subject pronoun io if you are drawing a strong contrast, like "I walk, but he runs."

Does in forma mean the exact same thing as "in shape" in English?

Yes! It translates perfectly. Just like in English, essere in forma means to be physically fit. If you wanted to say someone is "out of shape", you would say they are fuori forma.

Why use cammino here instead of passeggio?

Camminare is the general verb for the physical act of walking, which fits perfectly here since it is being done for exercise. Passeggiare specifically means to take a leisurely stroll for pleasure rather than for a workout.