Do I have to go through security and/or customs twice for a connecting international flight?

Both countries, Germany and the Netherlands are signatory to the Schengen agreement. The agreement has abolished the internal borders between 26 European countries. Passengers arriving from a non-Schengen country will pass through immigration control at the first airport of arrival in the Schengen area, hence at Frankfurt in your case. You will also pass through German customs with your carry-on baggage. However this is an easy procedure without formalities required like filling customs declaration forms. There are three lanes at customs; a blue lane for passengers arriving from other EU countries; a green lane for passengers who have nothing to declare; a red lane for passengers who carry items that must be declared (cigarettes, tobacco above duty-free allowance, or cash of more than € 10,000.00). You can just pass through the green lane if you have nothing to declare. You might be selected for a random customs inspection but that's hardly the case for passengers who travel on to another country.

Your flight from Frankfurt to Amsterdam is a Schengen internal flight without governmental immigration controls. You will pass a security check at Frankfurt before you can board your flight to Amsterdam.

Your checked baggage will be checked through from Philadelphia to Amsterdam; you will not see it in Frankfurt.

Once you arrive in Amsterdam you can immediately proceed on to baggage claim without your passport being controlled by Dutch immigration officers (since you have already been controlled at Frankfurt where you have entered the Schengen zone). Once you have collected your checked baggage you will pass through Dutch customs. The procedure is the same as in Frankfurt. You can just pass through the green lane if you have nothing to declare..

Gerd P is correct. You go through Schengen immigration in Frankfurt, which is usually pretty quick, and perfunctory customs. Then you have to go through security again. That used to be very slow, but the Frankfurt airport has improved it and when I've been there recently, it's been pretty fast, and there's a separate lane for people with tight connections.

in Amsterdam there's no immigration, just get your luggage and exit through the green lane.

I would think that once you go through customs once you will be fine, but if communications are bad then that might be not be the case. What I would do is ask for some sort of receipt at the first custom station inorder to avoid double fee's. Plus once you get into the country, I doubt a flight from one part of the country to another will put you in a terminal that will lead you to a custom's counter.

In Amsterdam is a wide spectrum of attractions for recreational and cultural sightseeing. They range from amazing previous structures, just like the Oude Kerk, to oddities including the Hash

only if you leave the international terminal secure area