- Which is always correct.
- That is not always correct. But when it is, it can sound more natural and remove ambiguity.
- When which introduces a non-restrictive relative clause, it cannot be removed.
- A non-restrictive relative clause can be distinguished by the fact that it is separated from the main clause by a comma. (Obviously this is only helpful if you know whether the comma, or its absence, is correct.)
- A non-restrictive relative clause is really another main clause, disguised as a relative clause in order to join it to the previous main clause. You can replace the comma by a period and which by it, and the sense is still the same. (Sometimes you need he or she rather than it, though in that case who is usually preferred over which/that.)
Let's test it with your example:
Here is a link to the article, which can be found on the Environment section of the website.
If the comma is correct, we are dealing with a non-restrictive relative clause and the following has exactly the same meaning:
Here is a link to the article. It can be found on the Environment section of the website.
Therefore, which cannot be replaced by that.
It's also possible that the comma is wrong and the author actually intended a restrictive relative clause:
Here is a link to the article which can be found on the Environment section of the website.
Then which can be replaced by that. In good style, to make it clear that the relative clause is restrictive, it's usually best to make this substitution:
Here is a link to the article that can be found on the Environment section of the website.
Using that is a much more subtle alternative to adding "(not the other one)" or "(not any of the others)".
Why the example is tricky
In this case it's not clear what the relative clause refers to: a link or the article. In both cases an interpretation of the relative clause as non-restrictive makes sense:
Here is a link to the article. The article can be found on the Environment section of the website.
Here is a link to the article. The link can be found on the Environment section of the website.
I personally think it's more natural to interpret the non-restricyive relative clause as referring to the article.
It's harder to make the problem explicit if the comma is wrong and a restrictive relative clause is attempted. But here is an attempt:
Here is a link to a specific article; to one that can be found on the Environment section of the website. (There are similar articles in the Economy section.)
Here is a specific link to the article; one that can be found on the Environment section of the website. (The main page currently has a different link to the same article.)
If one of these unusual meanings is intended, it's obviously a very good idea to use that in order to prevent the other, more straightforward readings. Even in context, absent-minded readers could get confused otherwise.