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.
Yes it would be very nice if more people would confirm our thoughts.
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")
Yes I need to reformulate it, i dont just care about brute force, but also other types of weaknesses, which might be present, but as a benchmark we only look at brute force.
Of cours if half of the cipher rounds can be broken then the security immediately halvens.
BUT just for simplicity we look at brute force vulnerability.
I mislooked D&T's post, thanks for corecting me.
That is only possible if you NEVER re-use an address. You should generate a new address EVERY TIME that you receive bitcoins.
Otherwise, the public key is right there in the blockchain for the whole world to see as soon as you spend an output that was received at the address.
Yes I know, probably need to include this advice in my guide too.