What should a pilot do when flying in the vicinity of parachute jumpers?
Qualification: I worked at a busy drop zone for 10 years.

Just announce yourself on the airfield frequency about 5-10 minutes out and they'll tell you what's going on, including which runway is active and how high they are jumping from - standard altitudes are 3000ft and 12,000ft AGL. At our place it was really simple: left-hand for 34, right-hand for 16. We landed everyone on the east side, and if we are dropping at 3000 all day you can just pop up to 4000 and be completely out of the way.

Under no circumstances make a cross-field pass as that's usually right in the middle of everyone else's landing pattern, and we don't carry radios.

If you are just passing by a 2km buffer is lots - no one is likely to be in the air that far away.

No reply usually means nothing in the air.