Transportation for 4 from Milan's Malpensa Airport to hotel in city/summer clothing advice

The easiest, quickest and least expensive way to travel from Malpensa to the city centre is via the Malpensa Express - https://www.malpensaexpress.it/en/ . That will take you to Milano Centrale in about 53 minutes. It also travels to Milano Cadorna in slightly less time. I'm not sure which station is closer to your hotel. Once you arrive at the station in Milan, take a cab to your hotel.

You can buy tickets at the airport but don't forget to validate them (time & date stamp) prior to boarding the train or you'll be subject to hefty fines which are usually collected on the spot.

Although none of you speak Italian, it would be helpful to learn a few of the relevant words such as Binario (track number). You may find some helpful tips in the RS Italy guidebook.

Most Italian churches require knees and shoulders to be covered, and some are extremely strict with that rule.

Privata Petria Gaggia is close to Rogredo station, and I see a Star Hotel Business Palace on that street. Seems an odd location to visit Milan, but the Porta di Mare Metro station is just around the corner.

This site gives taxi info for Malpensa Airport.
https://www.airportmalpensa.com/airport-taxi.php

Dress like a New Yorker or a San Franciscan and you'll be fine. I never heard of any no jeans thing, formal or informal. Just that Italians wear fashionable jeans, so not baggy and faded unless some designer made them that way. If you want to kind of fit in, darker rather than lighter colors, avoid the typical American look of denim shirt, khakis, and white sneakers. BTW here in Italy wild colors for sneakers are the thing; you see old guys in bright bright red ones.

Proper attire for Church is to have knees and shoulders covered. This applies to both men and women.

Otherwise, there is no 'fashion police'

how much should we expect to pay for taxi service? I

If you are staying in the city of Milan you'll pay the 95 € per car fixed fare. All included, 24/7. No tips, Milans' taxi drivers own the Medallion and make more money than you and me.

Would it be better to arrange for a towncar for 4 people

I can't think at a single European car model not licensed to carry 5 passengers. Anyway, if there is no spacious car in the taxi line, the other drivers will call one for you. Otherwise walk to the airport railway station, trains are cheaper at €14 per person and they can't get stuck in Milan's notorious traffic on the ring road.

Also, none of us speak Italian.

You don't need to speak Italian to print out the hotel's name and address and hand it t the first driver in taxi line. Add a big € 95 below it, just in case...

I've heard no jean or khaki shorts in Milan

Do you really think locals care how dresses the zillionth Mr/Mrs Doe they don't even notice during their daily lives? After two months there, and a couple of heart attacks, I stopped seeing even the 20 years old top-models walking around Milan: nobody will actually look at you.

Incidentally, the city is so hot and humid and miserable in July that literally everybody but cops, priests and top-models wear shorts.

that shoulders need to be covered, (women), if you go into a church

Men and women must cover knees and shoulders when they want to enter Catholic Churches all over Italy, even if that church can't afford to pay some guy at the door to enforce the rules. Nobody is interested in the way tourists cover knees and shoulders, just do it.

We were in Italy for 15 days in late May / early June. We flew into Milan and took the express train to Milano Centrale, and yes, you need to validate your ticket. If you don't feel terribly confident about this process, purchase your ticket (biglietto) from the ticket office (biglietteria) and they can give you instructions in English on where to validate and directions to the platform. When we landed the line for the ticket office was short. Public transportation everywhere we went in Italy (mostly from Naples northward) was incredibly easy to navigate even though it was our first time in Europe and my Italian is very limited. The regional trains have information in both Italian and English on the reader boards in the train and via the announcements over the speakers. Regarding attire, everywhere people were in shorts; EXCEPT most churches. While i did see men in shorts, the "shoulders covered" seemed to be enforced in most places. We were able to tour the Pantheon and my daughter and I had sleeveless shirts on, but the tour guide had scarves they let us use for the tour. My daughter's boyfriend and our son were able to go in with shorts on.

I think for 4 people it wouldn’t be extremely expensive to share a taxi rather than the train plus taxi from the station to the hotel.
The taxi fare is a fixed €95. Four train tickets from the airport to the city cost almost €60. How much you need to add for taxi from the station to the hotel depends on the distance. It could be €0 if you are walking distance and you don’t need a taxi or it could be €20 if a bit more distant from the station. So in the end I’d say that the train could save you at most less than €10 per person over the taxi all the way from the airport. If you have a lot of luggage, it might be worth the convenience over having to carry your suitcases aboard the train and rolling them up and down the station escalators.

Thank you everyone! This is very helpful information.
We are staying at the Starhotel as we have a tour departing from that hotel the 4th day of our trip. We were told that public transportation to the city center is very easy to navigate so it shouldn't be difficult to get to the sites we want to see. Since there are 4 of us, it seems as if getting a taxi would be easier with 4 peoples' luggage. We can only take 20 kg of luggage each on our tour, so we're hoping that we can all fit.
Yes, we do plan on learning some phrases before we go.

Yes, the M3 will take you straight to the Piazza Duomo.

take 20 kg of luggage each on our tour,

I would certainly do pre-trip test pack to see how well you can handle 44 pounds.