Dining question

You do not have to order both, or you can order both and split them. We sometimes share an antipasto then each have either a primo piatto, which is generally pasta, or a secondo (note secondi and primi and piatti are the plurals). Sometimes we both have the pasta and call it done. If the server does not speak English and you want to make it clear you want your dishes at the same time, you can say "Prendo il primo come secondo" which means "I'll take the first course as my main course." If you are sharing, say "Condividiamo il primo" which means "We'll share the first course."

You'll find portions are not huge so sharing both a pasta and a secondo is not insane. And you'll still have room for dessert.

We rarely order more than one Primi or Secondi each, and often a Primi for my wife, and a Secondi for me. I do not ever recall them serving my wife, and leaving me to wait for my dish. I think it is pretty obvious who is ordering what (I usually indicate my wife when ordering the pasta, and myself when ordering the Secondi) and that is our main dish...so they come at the same time. I suppose if you imply that you will share each, then they will stagger the serving, or at least will ask.

As for other general dining questions not asked...

Order a bottle of water (750ml), sparkling or still, it is nice to sip, in addition to wine, and slow you down, cleanse your palate, and everyone, locals included, will be ordering a bottle of water, the waiter will likely ask twice if you do not, and you will be the only table without.

The antipasti course can contain some real gems, at least look, try something different, we almost always get at least one.

Consider a side dish of vegetables, Contorno, the mains can be just the basic dish, not served with sides, and there are some great fresh veggies, steamed, grilled or sautéed.

Be prepared for the coffee question, it is almost expected you will end your meal with an espresso, try it, if you cannot, you will need to convince your waiter it is fine. I will have coffee sometimes, other times a digestif, like grappa or a liquor, especially if there is a local specialty.

I'm not sure water works the same way for people who order wine and those who do not. I see a lot of wine-drinkers with an open carafe of a water on the table; it doesn't look like something they've purchased. I only drink water, and it's not worth it to try to get a free carafe of the perfectly fine tap water. It seems a clear expectation that you will order something to drink, so I just order (and pay for) a bottle of water, emphasizing that I want still water, not fizzy water. The default in Italy is fizzy water, and I hate that stuff.

Consider a side dish of vegetables

We ordered grilled vegetables many times - the variations were interesting, and a well-prepared Cicoria Ripassata alla Romana can be a life-changing experience and change your opinion of chicory forever. Not to mention artichokes in Rome when in season.

the default in Italy is fizzy water

Where did you get this information? Still and sparkling water are always available and people choose between them depending on taste, I've never seen a "default" for frizzy water. In many restaurants, they start to introduce micro-filtered tap water which is usually served in carafe (still or fizzy); in any case, in Italy water is always included in the bill (or in the coperto).
Regarding the question before, ordering water together with wine is perfectly normal as wine is an alcoholic and "heavy" beverage and people don't just drink that for the whole meal, especially if they have to drive.

Fairly often I've been served fizzy water even after ordering still water; that's why I assume the fizzy stuff is considerably more popular. In any case, my admonition to make one's preference known stands.