It's not that bad. You will be shepherded through an arrival hall at JFK where you have to pull your bag off the belt. Give the customs person your blue form declaring any gifts you intend to leave in the USA. Then just after Customs will be another belt where you drop off your bag again (if it already is tagged to your real destination).

When you check in your bag in Milan, be persistent and try to get it through-tagged to LAX; but Alitalia sometimes won't do that if you are on two different carriers. No problem... just talk to any agent after Customs and they will replace your bag-tag.

Yes, they do allow enough time for this process if you have booked a normal connection. But normal rules apply; always carry one day's worth of emergency provisions in your carry-on, and put multiple tags on your bag with your destination contact address and mobile number.

Thank heavens you're not connecting through IAD... it still works at Dulles, but they are so rude there it takes some of the fun out of the trip.

Once you arrive in LAX there are no more formalities.