I'm trying to sort out the difference between 免费 and 无偿 as adverbs. Would you say 水果店的老板免费送了我六个苹果。 or would it be 无偿送了？
Strictly speaking, '免费给了我六个苹果' means he gave you six apples for customer relationship for reasons like you're a frequent customer or you just make a bulk purchase of other stuffs. '无偿给了我六个苹果' means he gave you six apples out of kindness because you lost your wallet or you're starving. In spoken language, however, their usages are usually mixed and both of your sentences are fine.
BTW, '送' already implies 'for free'. So '免费送了' is unnecessary repetition but again sounds fine in spoken language.
Update: As the other answer pointed out, 无偿 is almost never used in Hongkong which indicates that the usages can be highly regional. Something to keep in mind.
Generally speaking, we use "免費" when someone gets something for free, and "無償" when someone does something for free.
On the other hand, we do not say "無償" in Hong Kong. For example, we say "捐血" instead of "無償獻血", and "義務工作" instead of "無償社區服務".
From a Taiwanese point of view (MOE), at least, 无偿 is determined by law.
In some other places it's used with 赠与 to mean "grant" or "outright."
OCE also lists this under the English entry voluntary
Where as 免费 would certainly not involve law and would just, simply, mean "free."