I am astonished at your questions. Why on earth wouldn't people wear jeans, sunglasses, or scarves in Europe?
First up, Europe isn't a country.
Second, there are regional differences in what people wear simply because the weather and temperatures vary greatly. What you wear in Ireland in July is CONSIDERABLY more than what you'd wear in Italy in July.
The only rule about short shorts and short skirts is that we really don't want to see your knickers or whatever else you've got underneath there. And please don't wear those short shorts that show off half your bottom, you could easily be mistaken for a prostitute in some places. Obviously if you're going to a nice restaurant for dinner you don't want to look like a tart, but you don't have to buy a ballgown either. You can wear whatever you think is pretty. However, when going into places of worship - of all denominations, I stress - you will be asked to cover your legs, cleavage, waist and shoulders as a sign of respect, and it's not just women who'll be told to do this either. If you're entering a mosque, you'll be asked to remove your shoes and you might be told to cover your head. You can wear converse, kids here wear those.
And forget about trying not to look like a tourist. As soon as you open your mouth to speak you'll be outed. Just resign yourself to this inescapable reality, and enjoy your visit. In any case, all those places have been receiving visitors from the US and other places for several hundred years now, and will go on receiving them long after you leave.
You absolutely shouldn't forget comfortable walking shoes. You'll be doing a lot of walking, and unfortunately converse aren't so great for that. Make sure you have good sturdy shoes with proper arch support, you'll be glad you did.
The temperatures in Italy depend on when you're there. but will often be over 90 deg F in the summer and sometimes can be above 100 deg F. Some of the churches, like St Peters in the Vatican have dress codes requiring that you have your shoulders and knees covered; these are enforced strictly in most places. You won't see a lot of Italians wearing shorts in the tourist areas; they tend to be a little more formal when away from home. People certainly do wear sunglasses; there are lots of designer sunglasses places. Take comfortable shoes for walking for all the sightseeing you'll be doing and break them in before you go.
The one place where you might possibly have any trouble would be in trying to go into the Vatican or possibly some other Catholic churches--you have to dress at least a little conservatively (which if I recall means no bare shoulders or ultra short skirts/shorts for women). The exact rules are undoubtably online.
Pretty much anything you want is fine. But I think those big hats look really touristy for some reason. I feel like no matter what you wear, the people in those countries know you are tourists.
Wear something u would normally wear when you go to school. Hip & trendy or casual. Except shirts or sweater w/ U.S states logo. Scarves & shades are ok. Do not wear fanny pack or bumbag (UK version) it depends what month. Summer in England is unpredictable. It can be rainy during summer. Bring cardigans just to make sure