the pedal problem is most likely a bad freewheel. the freewheel is the gear on the back wheel that has the bicycle chain on it. remove the rear wheel and see if the freewheel spins freely in reverse and engages in forward. sometimes spraying some wd40 or any penetrating oil in it will help it to work. what happens is there are two spring loaded clutch dogs inside it. they get dirt or rust in them and they stick in a down position. when this happens, the frewheel wont engage. you can take the wheel to any bicycle shop and they can remove your freewheel and you can buy a new one from there. the cheapest place to buy freewheels is www.danscomp.com.
as far as the power transfer from the engine goes, it sounds like your clutch is not engaging. it is located under the plastic cover on the left side of the engine. it is a centrifugal type like a mini bike would use. look at it to see if every thing is moving freely. also check your belt to be sure its properly tensioned. there is a batavus service manual located at www.mopedriders.org in the moped repair section. it is for a 76-78 va50, but i think the hs50 also applies.