Is it necessary to put the "ne" always in front of the verb?
Tio ne estas via afero.
Or could I also say
Tio estas ne via afero.
As it comes more naturally to me as a german native. I know that Esperanto has free syntax, but figured it might be necessary to have the negation occure before the finite verbform.
You are correct, jcreed. "Ne" is not flexible in position as it always goes before the thing it is modifying.
But its not negating the state of existence "ne estas", but the fact that it isnt "ilia afero". So in the case with estas it would even be wrong then, which is obviously is not. This is where my confusion stems from.
Mi ne acxetas vian aferon. Mi axcetas ne vian aferon. -> The flexibility for ne here is not giving, but with estas it sure seems like it.
I keep reading your example sentences but I don't see a difference. (Except I've never seen the second one, with ne after).
Ne always comes before what it negates and it's usually a verb.
Here's a example from PMEG (http://bertilow.com/pmeg/gramatiko/neado.html) about negation: - Ne miksu vin en aferon ne vian!
So, in regards to your example -> "Mi aĉetas aferon ne vian." That looks ok to me.
What it is negating is "estas via afero". Don't split it up.
I have found a reference, which you will probably not be able to check at the moment, and it certainly doesn't explain more than "this is the rule", but here it is for what it's worth. This is a very good and well-respected work, by the way.
"Step By Step in Esperanto" by Montagu C. Butler: pg. 30, para. 88: "Ne precedes the idea it negatives."
But you can change "ne estas via afero" to "estas ne via afero" to even "estas via afero ne" without an actual problem. I could even say "Ne tio estas via afero" or "Ne afero via estas tio" without changing the meaning. Sure, not everyone is used to the syntax, but gramatically it still works, as for emphazising nuances or just bringing in your native syntax (which esperanto often advertises itself with)
like the only things that need to appear together are via and afero, again in free order
It is not your business. It is not your business (by contrast and for emphasis, it is the business of somebody else) It is your business. (The "ne" afterwards would precede the thing that follows it that it is negating.) (You will come across a looser order in song lyrics and poetry, but they're allowed to mess with rules and shouldn't be used as a guide for regular use.)
How about this. Make a note of your concern(s). Continue with the tree and go on afterwards to study other courses, use Esperanto in actual conversation, and so on, and if it's still an issue for you then, you can perhaps find a source whose explanation you can accept. I can do no more at this point other than to refer you back to the citation from a respected grammar guide.