If you drop a feather into the atmosphere from orbit, will it burn up or fall to the ground?

I would have to guess, yes, but it all depends on how fast they are moving. Most of the meteors you see at night are smaller than a feather and are the size of beach sand, yet at 30 kilometers/second they burn up spectacularly. A feather weighs many grams and should likewise burn up in an even more dramatic meteor. The problem is that the orbital speed of the feather is 10 kilometers per second or so, and this speed is added to any speed you have to give it to 'drop' from orbit.