customs/immigrations check at Frankfurt - Milan

Correct. If you have checked baggage it will you won't see it until you arrive in Milan; it will be automatically transfered to your connecting flight. Also, in Frankfurt you will have to go through another security screening, so make sure your carry-ons are in compliance with EU rules.

You WILL be subject to a customs check of your bags in Milan. However, these days they often let you pass through without a detailed check if you have nothing to declare, but they could check you.

We had a similar Star Alliance transfer in Frankfurt for our flight to Florence. We were on Lufthansa. Interestingly, we did go through another security area in Frankfurt but they didn't check our carry-on, just our ID and tickets. We were still in the overall secure area of the airport.

What surprised us the most is that we did not go through any customs in Florence. We picked up our luggage, kept looking around for customs, didn't find any so we walked out the door. We kept looking around to see if we were going to be arrested or something. Nothing happened. This must be a rare occurence because we always encounter customs of some type.

I have flown into Germany 6 times (FRA x 4, MUC x 1, STR x 1) this decade, and I have never been to customs (over there). After clearing immigration, as I am walking out, I see a sign for "Baggage claim", but since I have only a carry-on, I walk on by and out the door.

Well theoretically you go through immigration in Frankfurt and through customs in Milan, right after retrieving your bags. In Milan you should use the channel saying "coming from outside the EU" since this is your original departure point. But these days, customs in Europe is more or less non-existant, and chances are around 98% that you will be waved through or that the customs booths are unmanned. In some airports, you don't even realise that you just have been through customs!