When are 'each' and 'every' not equivalent?
Solution 1:
Mostly, each is used with an identifiable set. In I gave each child an apple this is clear as the set of children you gave apples to is known to you and will not change. Conversely, since we've no way of knowing which years are specified in I go there every year, it would be unnatural to use each in this sentence. Even you, the speaker, have no way of knowing the exact set of years here as it's expressed as a state which continues indefinitely.
Also, the distributive meaning is stronger with each. In I gave each child an apple there would seem to be clearly differentiated acts of giving involved, as opposed to, say, giving one big basket of apples to a group of children. Though I'd say I gave every child an apple could still have the same interpretation.
As to your question about when each and every are not equivalent, there are some clear limits on when exchanging one for the other is acceptable, and when it is not.
Each was given an apple.
* Every was given an apple.
I gave each of them an apple.
* I gave every of them an apple.
As you can see, every cannot be used as a fused determiner-head. If we insert one into the sentences above, the ones with every become acceptable again.
I go there practically every year.
* I go there practically each year.
Every can be modified, but not each.
The two children came and each one was given an apple.
The two children came and every one was given an apple.
In the first sentence, it seems that we are talking about the two children who came as each may be used with a set of two. In the second sentence it doesn't seem to be the two children only that we're talking about as every is not acceptable with sets of two.
They were hanging on his every word.
* They were hanging on his each word.
Following a genitive determiner, every is acceptable, but not each.