Learn Italian: Porto la borsa su una spalla. - I carry the bag on one shoulder.

Yes, but the verb portare is very flexible. It can mean "to bring", "to carry", and even "to wear" (when talking about clothing, accessories, or glasses). In this context, "I carry" or "I wear" makes the most sense for a bag.

Why are su and una written as separate words instead of combined like sulla?

You only combine prepositions (like su) into a single word when they are followed by a definite article (like la, il, i). Since una is an indefinite article, it stays separate. "On the shoulder" would be sulla spalla, but "on a shoulder" is su una spalla.

The English translation says "one shoulder", but doesn't una mean "a"?

In Italian, the words for "a/an" (the indefinite articles like un and una) are exactly the same as the number one. Context tells you which makes more sense in English, but the Italian remains exactly the same whether you mean "on a shoulder" or "on one shoulder".

How would I say "on the shoulders" if I were carrying a backpack instead?

You would use the plural form spalle (shoulders). Because you would typically say "on the shoulders", you need the plural definite article le. You then combine su + le to get sulle. The phrase would be sulle spalle.