Shorena is giving answers at least as good as I could.  There's nothing I can offer beyond what he's already said.  GMaxwell or Death&Taxes might be able to give better details or correct any errors.

I think a big part of the problem here is that words are being used without a clear understanding of what those words mean.

In the original post, you talk about three different examples "for brute forcing".

If you are talking about brute forcing (trying every possible input value until you find the output value you are looking for, then key size (or rather total possible values) is what you are talking about.

If you are talking about weaknesses in the algorithms, and techniques that take advantage of those weaknesses, then you're more interested in level of security.

Entropy is typically a measure of randomness.  (You'll notice that D&T doesn't say "bits of entropy", he says "bits of key STRENGTH")