Milan to Monterosso

Yes, many daily connections. Take the Malpensa Express train from the airport to Milano Centrale station (careful, NOT Milano Cadorna station which is also served by different Malpensa Express trains). There are hourly connections to Monterosso. The ones at 12:10, 2:05 pm, 4:05 pm, 6:05 pm are direct with no need to change trains. Takes about 3 hours from Milano Centrale.

Yes, that's actually a very easy connection. You'll first have to travel from the airport to Milano Centrale via the Malpensa Express, and then connect with one of the trains to Monterosso. You can buy tickets for the entire route at the airport rail station, either at a staffed ticket window or using one of the Kiosks.

There are numerous trains from Milan to Monterosso each day, but many of them have one or more changes which would be a bit of an ordeal after a long international flight. However there are a few direct trains and if you can connect with one of them, it will be an easier trip. There are direct trains at 12:10, at 14:05 and again at 16:05 (and later) and many others with changes. You can check all the departure times and other details using the bahn.de or Trenitalia websites.

When were you thinking of travelling "next spring"? I'd suggest getting hotel bookings as soon as you've set your travel dates.

Also, be aware that Milan has two airports. Milan Malpensa is the one that gets nonstop flights from the United States. If you are changing planes in Europe, you may land at either Milan Malpensa or Milan Linate. Linate is closer to the city, but does not have a train connection. You would take a bus or taxi to Milan Stazione Centrale, then a train to Monterosso as described in the posts above.

You're on the right track with that advice.

All I would add to this, having just done this, is it is a long and exhausting day.