That is saying "It is not soldiers that I know." I'm not sure the English sentence is trying to express that.

It's 'any' because katonákat doesn't have an article (a /az) .. which would make it 'the' soldiers.

Since we are not talking about specific soldiers, it could be 'any' soldiers.

That's acceptable.

It does, yes. The word order rules are slightly complex, but learnable. The biggest problem is that you have to throw your Indo-European assumptions about word order over board. :)

It's relatively simple in this sentence. You have four words you can juggle around (I'm including the én here, which is not necessary in this sentence anyway), one of which is a negation. Negations are pretty important things, so they tend to be put towards the front.

The word that follows a negation is, unsurprisingly, the one getting negated. Now what do you want to negate?

• Nem én ismerek katonákat. - It's not me who knows soldiers, but Csilla might know some.
• Én nem katonákat ismerek. - It's not soldiers that I know. I'm only familiar with tanks.
• Én nem ismerek katonákat. - I do not know soldiers.

The last option is the most common, neutral one. You're just stating that you aren't familiar with any soldiers. (Parallelly to the other options, with the right emphasis you could also say "It's not knowing what I do with soldiers, I just acknowledge their existence", but that's a bit more out there.)

The other two options can work on their own, but they need good context or additional information to make proper sense.

Now, let's go for the "nem ismerek" variant. What can we do with the other two words? Well, almost anything. The above sentence is the most likely one, with an emphasised subject:

• Én nem ismerek kantonákat. - I do not know soldiers. Do you?
• Katonákat nem ismerek én. - Soldiers? I don't know any.
• Nem ismerek kantonákat (én). - I don't know any soldiers.
• Katonákat én nem ismerek. - Since we're talking about soldiers, I need to say that I don't know any.

The baseline is: the farther in front something is in the sentence, the more important a piece of information it is.