Can I transit thru Shanghai Pudong on separate tickets ?

If your entire layover in Shanghai is less than 24 hours you will be eligible for 24 hours visa free transit. 144 hours visa free transit is granted only when your layover in mainland China is longer than 24 hours. In any case, you will have every possible ability to move outside the airport and to enjoy this facility.

Upon arrival in Shanghai, you will approach to 24/144 hours visa free transit counter where you will ask for temporary entry permit where you will present them your flight itinerary. By the way, traveling on separate tickets is definitely not a problem, but quite a normal occurrence. When you present your flight itinerary, you will be allowed to leave the airport and later to check-in to another airline to proceed on your flight itinerary without a need to have any kind of visa.

You will be just fine... You should have just your flight itinerary at hand and everything else will be just a formality.