Is it possible to have these salts alone in the mobile phase without adding an acid (say acetic acid) to it?
Yes, but then you will have a salt solution, not a buffer. In order to be a buffer, the weak ion (in this case, acetate) must be *partially* dissociated so that it can both donate and accept protons. In other words, an acetate buffer must contain significant levels of both the acetate (ionized) and acetic acid (unionized) form.
When a method calls for a buffer, like ammonium acetate, is it assumed that you use the weak acid to bring it to the need pH?
Yes, but there are a couple of "gotchas". If you are trying to buffer near the pKa of the acid (4.8 for acetate), you could do it by adding acetic acid, but that would increase the concentration of acetate. It would be better to start with acetic acid at a known concentration and add ammonium hydroxide to adjust the pH upward. If you were trying to buffer near the pKa of the base (9.4 for ammonium) it would be the other way around.
add a salt like KH2PO4*H2O which makes lets say a pH 6 buffer, why then do you need an acid?
Because it won't be a buffer and it won't be at pH 6 (probably more like 4-5). For pH 6 you would either use a appropriate mixture of the mono basic (KH2PO4) and dibasic (K2HPO4) salt or else start with the monbasic and add KOH as necessary to bring the pH up to 6 (by the way, pH 6 would be on the ragged edge of usability for phosphate (the pKa for the second ionization is listed as 7.2).
And why can you make a buffer with the previously mentioned salt and K2HPO4*7H20, without having to add an acid or base?
You can't. I suspect the issue here is that not everyone uses the word "buffer" correctly. I know people who use "buffer" to describe *any* mobile phase (e.g., "the buffer used for the separation was 45% acetonitrile / 55% water").