Almost there 
two last problems only one of which I know how to fix: your silkscreen doesn't display (fixable) and your holes are now too small (don't know how to fix that in Illustrator) so I copied a correct size one made in Inkscape in to your pcb. The silkscreen is easy (although finding it took me a while), the id in the svg is Silkscreen, it needs to be silkscreen (all lower case) to match the fpz file which is apparently case sensitive. While the Inkscape hole ( id connector1pin-6 which you need to delete when you get this fixed) in the pcb works correctly, setting the same parameters on the existing holes doesn't work so I don't know how to fix that (hopefully you will, via experimentation if nothing else ). To see your hole sizes with the part loaded in Fritzing and pcb selected (and the board within the grey area as parts out side the grey area will be truncated which has tripped me up more than once.) click file->Export->For Production->Extended gerber and set an empty directory then click select folder. In that directory there will be a file called Untitled Sketch_drill.txt which is the text drill file. Mine for this part looks like this:
; NON-PLATED HOLES START AT T1
; THROUGH (PLATED) HOLES START AT T100
M48
INCH
T100C0.038022
T101C0.022900
...
The first one is my hole from Inkscape at .038 (and a bit) the other is your 6 holes at .022 that you need to convince to be .038 like the first one somehow. Hope this helps.
Peter