How many days to tour Milan?

This is way too much for one day unless you are just going to look at things from the outside.

I'd get a timed entry to Santa Maria Delle Grazie for the Last Supper for as early as you can manage. There was an English tour at about 930 or so, I think. That will take about 45 minutes to see BUT you need to be there a certain amount of time ahead so you'll probably wind up with 1.5 hours here. Buy your ticket from the official website as soon as they go up for sale.

The Duomo, if you do the Rooftop and see the interior takes a couple of hours. Get the Fast Pass to take the elevator to the roof but then you'll have to walk down. The fast pass comes with entry to the museum across the square but I didn't have time for that.

Afterward you can walk thru the Galleria Vittorio Emanuele to La Scala and see it from the outside (did you want to go in?).

I added in the Pinacoteca Ambrosiana which is near the Duomo but did not do anything else on your grocery list.

What is it about the sites you have listed that makes you want to see them? For myself, I wanted to see Leonardo's work before it completely flakes off, wanted to see the Raphael cartoon (drawing) of the School of Athens in the Pinocateca, and wanted to do the rooftop and interior of the Duomo. I was looking for somewhere to sit and eat dinner so walked thru the Galleria for that.

We spent about 6 hours at Castella Sforesco. There are several different museums there.

We spent 2 nights in Milano. Probably could have stayed 1 more night. It's an expensive big city.

I'll also add that you have to figure walking time or transportation between sites as well. It took me just under 30 minutes to walk from near the Duomo to Santa Maria Delle Grazie, then of course, 30 minutes to return to that area.

To do everything on your list you'll need at least 2 full days, especially if you want to do the museums at Sforza Castle. Parco Sempione is a nice park to walk through and I think there's an aquarium and botanical garden. I haven't been to either but spent my arrival day people watching at the park and getting over jet lag. Similarly the Galleria Vittorio Emanuele is some place to just walk through unless you are actually shopping. I agree with Pam that you should add the Ambrosiana Library to your to do list. You may also want to add the Duomo museum to your list. It's included in the admission to the Duomo itself.

Is this the website for Last Supper museum? It seems to me that the tickets are only available on Dec 20 and 21. Am I right?

https://cenacolovinciano.vivaticket.it/

In addition, for Duomo di Milano, Fast track private tour Cathedral, Archaeological area and Rooftops takes about 1.5 Hour. May I ask how long do I still need for visit after this guided tour? Thank you!

"Is this the website for Last Supper museum? It seems to me that the tickets are only available on Dec 20 and 21. Am I right?"

Yes, that is the correct ticketing website. And yes, it looks like for December there are only tickets left for 20 and 21 but many times available during the day.

I did not take the guided tour of the Duomo, but if it covers all those areas then you probably don't need a lot more time there.

Given unavailability of tickets, how about to use guided tour for last supper museum (see link below)? Are they trustable?

https://www.viator.com/Milan-tourism/d512-r15707886251-s198003611?mcid=28353&tsem=true&supci=1053746412&supag=15707886251&supsc=aud-470357328126:kwd-88110020891&supai=275935345586&supap=&supdv=c&supnt=g&supti=aud-470357328126:kwd-88110020891&suplp=9032014&supli=&m=28353&supag=15707886251&supsc=aud-470357328126:kwd-88110020891&supai=275935345586&supap=&supdv=c&supnt=nt:g&suplp=9032014&supli=&supti=aud-470357328126:kwd-88110020891&tsem=true&supci=aud-470357328126:kwd-88110020891&supap1=&supap2=&gclid=EAIaIQobChMInoi0jsqKggMVhM7CBB3CrgmxEAAYASAAEgIjPfD_BwE

May people do wind up going with a guided tour because they can't get tickets. I'd not buy thru Viator though. It's a 3rd party ticket reseller. On each of the tours listed if you click on Additional Information the name of the actual tour company is listed. I would book directly thru that tour company instead of adding the layer and middleman of Viator.

In looking at the first one that comes up for me it is a Skip the Line tour of the Last Supper (no other sites except the actual church next door) and it is showing as 53E on the Viator site and 46E on the WanderItaly site.

Viator is a third party reseller
They do not actually operate any tours

Book directly with tour companies you can trust

Walks of Italy is one
https://www.walksofitaly.com/milan-tours/

Seeing The Last Supper is important to many
It may not be important to you

Viator provided free cancellation. However, I didn't see the cancellation policy on wanderinitaly.com. I generally prefer these third party sellers because of that. Just like book hotel via Expedia or booking.com rather than go to individual hotels' website.

https://www.walksofitaly.com/faq/
https://www.walksofitaly.com/cancellation/

Sorry. The seller is wanderinitaly not walksofitaly.

Walks of Italy offers tours in all the cities you are visiting

They usually offer discounts if you book several tours with them

Also ask for their Rick Steves discount

Sorry. Walks of Italy doesn't have the tickets on my days in Milan.

The $85 tour is provided by wanderinitaly.com. However, its own website actually only charge 68 euros BUT has no cancellation policy at all. Do you think this tour is trustable or not. I already booked this tour via viator.com. But I worry this tour may not be trustable.

I don't know if wanderinitaly is trustworthy. I'll just note that at today's exchange rate 68 euros is $72. So the mark up pays the foreign exchange fee, the third party provider and the cancellation risk.

This tour provided by wanderinitaly.com is listed on Viator with 1107 persons' rating and Getyourguide with 3476 person's rating. Both gave over 4.5 rating. Getyourguide is cheaper ($81). The wanderinitaly.com itself doesn't provide free cancellation info. Both Viator and Getyourguide do.

https://www.viator.com/tours/Milan/HISTORICAL-TOUR-OF-MILAN-skip-the-line-LAST-SUPPER/d512-33060P2

https://www.getyourguide.com/milan-l139/milan-historical-tour-the-last-supper-t62890/?ranking_uuid=b5e9e838-f9ff-471a-980e-526e8c33239b

I researched a little bit and found the next tour provider with their own website and explicit cancellation policy is this one

https://citywonders.com/milan-tours/last-supper-tours

But this company is based on Ireland (Wanderintaly is Milan based. This tour includes both Duomo and Last Super museum in 3 hours. That seems to me it is too short.

Other than City Wonders those are all third party resellers that are selling you a voucher for a tour they do not operate.
If they can guarantee you that they DO have the Last Supper tickets already- then fine. I don' think that is the case though.

The reason Walks of Italy- a well known tour company with good reviews- doesn't have your dates is because they do not have tickets.

There is always the chance of your tour being canceled by the seller because they oversold vouchers.

What date are you looking for?
The Last Supper is closed on Monday.

This tour includes both Duomo and Last Super museum in 3 hours. That
seems to me it is too short.

All visits to Last Supper are time limited- 15 minutes. Add a bit more for arriving early and the prep before you go into the room, so at most you'll spend an hour there.

I plan to take this one Duomo di Milano, Fast track private tour Cathedral, Archaeological area and Rooftops. I don't know if City wonders' Duomo tour cover rooftop (I guess no).

Another strategy is to buy both in separate days.

I believe wanderinitaly.com is not a reseller. But no people on RS.com mentioned it before.