Many thanks to all the replies for the great contribution. I spent a whole afternoon at a LBS with a professional mechanic to have all the possibilities mentioned above carefully checked and tried all the methods suggested. Pity the problem in my situation hasn't been solved.
Chain is NOS stuff. we checked every link and roller, they are in great working condition, also tried to have it shortened, twice; The smallest sprocket teeth are also in very great shape,no bent,only little wear,(judged by eye and limited experience). they bite very well with the chain;Derailleur hanger was checked, it's aligned, sorry for the poor pictures I provided, the flash of camera seems to make this part misleading;The rear derailleur looks not tweaked,and shifts very well,but is in a low spring tension because of aging, a condition that the mechanic had thought was the reason to cause chain skipping in my situation.we tested it with a method of tying the RD cage with a string to the ring of quick release nut in order to fix it in a tightened angle.but it didn't work neither.
It seems in a situation beyond my ability to solve the problem for the moment, I may have a double check this week, or swap for a rear derailleur with higher spring tension to give a try. Not considering abandoning the chain and freewheel yet. They are really beautiful on my bike. Thanks again for all the help offered. Really appreciate.