1) I'm trying to build a tower-area above the main fort, but the wall is split between columns and fortifications, and walls and fortifications. Any idea why it's doing this/how to fix it?
The good news is that at least two of those circles are not pillars, they're the end of your wall. The "+" signs are floors. (Use <k> to examine and determine exactly what they are - Supports (aka columns/pillars) and lone walls look the same.)
As for the rest, you're being sloppy with your designations, which can be easy to do. Somehow you hit a mix of <b, C, F> for fortifications, and <b, C, f> for the floors. (And possibly <b, S> for a support/column.)
To remove a Construction, you have to <d>esignate it for removal - <d, n>. This will probably take longer than it took to build, and any dwarf might decide to come fill the task - no labour controls it.
Once it's gone, be more careful w/ your Construction designations - <b, C, _ >. Once you place one type of construction, you are still in the construction menu, but must re-select which sub-type - <w> for more walls, <F> for fortifications vs <f> for floors, and so on.
You can also put a "line" of up to 10 of the same designation at once by using the u, k, m, h keys to change the dimensions of the designation before you place it - I'm guessing you designated each of these tiles separately. (a single line of Fortifications would be approp, methinks - liberal use of the < u > key before placement.)
(If you are 100% sure it was all designated at the same time, then it's a bug.)
2) When I was trading goods, the trader said something along the lines of "With things as they are, I can't fathom you ending up with these goods" when I offered the trade the first two times. When I offered the trade the third time, he accepted. What does this message actually mean?
I don't believe he accepted the same trade - if he made a counter offer, he changed the items you were offering, adding (considerably!) to them. But what that particular message means is that you are nowhere near an acceptable offer.
You need to offer a value of about 2:1 at first for trades. You were probably offering, not quite at a loss for him (which he ignores with a "are you joking?" sort of response), but close to it.
3) What should I try and focus on next? I was reading up on the Dwarven economy but that seems really far away. I still only have my original 7 dwarves. How long before I have to worry about military?
I'd suggest "created wealth", to help immigration. CW is found on the z-menu, in the left hand column. The more CW, the more migrants - once they arrive, you can select some for your military. (I like to produce steel armour, which is both valuable and necessary for the military. Statues/mechanisms of valuable ores work too, as do prepared meals. Lots of options.)
EDIT: Also, I just found out my dwarves are storing cooked food in my seed stockpile. The only thing allowed in the pile is seeds, but they're doing it anyway(fustrating because there are plenty of open spaces in the food stockpile)...
<q, s> for customizing the stockpile - there is a switch in the lower right for Prepared Food, < u > - turn that off.