Rail questions

First, you're actually travelling only in four countries covered by the Eurail pass....it is not good in the UK. The Dutch Flyer is a cooperative program between the National Express East Anglia rail company in the UK, the Stena Line ferry company, and the Dutch rail service, NS. A Eurail pass will give you a 30% discount on the ferry itself (full fares, not discounted ones) and, of course, be used for trains on the Dutch side. But you'll have to purchase your British train ticket to the port at Harwich, and using the pass on the Dutch side for a relatively short train trip will cost you a day off your Eurail pass. On the Dutch Flyer website, a ticket from London to Amsterdam, including a cabin on the ferry, is only about $75 per person.
Second, you can check schedules for the Netherlands (and most other places in Europe) at the German national rail service, Deutsche Bahn . The trains you're concerned about do run on Sundays and they don't require any special supplements or reservations, so the Eurail pass will work just fine. The run from Hoek van Holland to Amsterdam costs about 19 Euro if you purchase point to point tickets.
Third, you can't "subtract" a country just because you're not stopping there...after all, you are still using their rails. Luckily, though, Belgium is covered under the Benelux portion of a Eurail pass (Belgium, the Netherlands and Luxembourg are considered one "country" for the purposes of a Eurail pass.) So, essentially, you'll only have to purchase a pass covering three countries....Benelux, France, and Italy.
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Fourth, RailEurope, the place you'll probably have to go to reserve the overnight Paris-Venice train, offers couchettes in a six-person compartment for second class for as low as $39 per person, plus a day's cost of your pass. The regular fare for similar accommodations is about $155 per person. For any sort of privacy, a first class double compartment is going to cost you a lot more.
You may want to do a little more research, and check out the Dutch Flyer, NS Rail, Thalys, and TGV Europe websites to better price out these options. You can use RailEurope to cost out your pass plus reservations, which will be needed if you use a pass on the Amsterdam-Paris trip, and the Paris-Venice trip.

"First of all, I wanted to confirm that transportation from Hoek van Holland to Rotterdam runs on Sundays. Then I wanted to let you know I’ll be taking InterCity train from Rotterdam to Amsterdam, leaving Rotterdam Centraal daily at 08:58 and arriving Amsterdam Centraal at 10:03."

My thought is that you're over thinking a lot of this. First, yes, there will be trains on a Sunday from Hoek van Holland to Rotterdam. Realize that even if you miss one train in the Netherlands, they run so frequently that you would likely only have to wait an hour to catch the next one.

Second, "Eurail" is just a travel agency that sells tickets and passes for some national rail companies. Their website will never show all of the available trains.

Third, you're trying to do too much in too little time, especially flying in from the West Coast. You are spending too much time in transit and you haven't accounted for jet-lag. If you haven't bought your airline tickets yet, I would suggest flying open jaw so you don't have to double back all the way from Italy. I also would consider that if you really want to see Italy, drop either the Netherlands or Paris and fly on a discount airline to Italy. Or, drop Italy instead and save yourself the longest commute of your trip. Either way, I would seriously consider doing some paring down.

As Steve and Norm have explained, you'll be better off booking the Dutch Flyer Rail & Sail combo on its own.

Seat reservations for Thalys trains are required and are included in the price of point-to-point tickets. You would need to buy separate tickets for Amsterdam-Brussels and Brussels-Paris. Standard fare tickets are expensive, but Smoove fare tickets booked well in advance online (up to 90 days allowed) at www.thalys.com can be as low as €25 for Amsterdam-Brussels and €25 for Brussels-Paris.

If you book well in advance (up to three months allowed) at www.tgv-europe.com, you can pay as little as €55 for a bunk in a six-person couchette or €65 for a bunk in a four-person couchette on the Paris-Venice night train. These are P2P ticket fares. Spending a little more is well worth it for the extra elbow room.

Note: If you stick with buying a railpass, even though you'll go through Switzerland on the Paris-Venice night train, your pass does not have to include Switzerland for that particular train.

You can take trains from Venice to Pisa (with a connection in Florence) for under €50. This is the walk-up fare and includes a seat reservation on a high-speed train for the Venice-Florence leg. (The Trenitalia site does not accept US credit cards, but the station ticket machines do.)

Finally, even though I've listed the best fares for the routes as you presented them, I'm with Tom. Fly open jaw (multi-city) to avoid backtracking to London. And either cut something out or add more days to your trip so you'll have a better balance between travel days and sightseeing days. It takes longer than you might think to get from a station to a hotel, check in, and get familiar with a new city--all of which you need to do before you can start sightseeing.