This is really a three part question, I'll try to answer it appropriately
What airlines fly into Milan Malpensa airport (MXP/LIMC)
The first place I'd start is the arrival and departure info for the airport itself. A quick glance shows the usual european low-cost operators (EasyJet, Wizz & Ryanair) as well as the larger operators (Emirates, British Airways, American, Singapore, Air China, Lufthansa, Cathay Pacific and of course, Alitalia!).
You can also check out the airport's wiki page which has a helpful section on Airlines and destinations served by the airport (direct link).
What do the liveries of specific airlines look like
I'm not sure you'll find a single handy pdf with all these on, but again wikipedia has some helpful information - indeed a specific list of airline liveries and logos. Cross reference this list with the one above and you could pull together a helpful cheat-sheet of all the ones which fly into LIMC.
How do I identify different types of airliner
Thankfully, the list of commonly used airframes is reasonably small, unfortunately with quite a fair number of variants of the same model if you're trying to be exact.
Once again, wikipedia will give you information about each of your chosen airline's fleet, and you can check arrivals and departures on something like flightradar24 to see which aircraft are flying which route.
There are websites dedicated to the art of identifying commercial airliners such as airlinespotter.com and aircraftrecognitionguide.com.