I can't seem to export my drawing to SVG correctly. When it opens in illustrator most of my objects are hidden, but in illustrators outline mode i can see all of them. What am I doing wrong?

My drawing can be found here

I've done a little bit more tests and it seems that transparency and shading is not applied at all to the objects in illustrator.

Also when I have an image inside of an object it is not transferred to illustrator.

Another thing is if I use splines to make curvy lines with arrowheads in them, the lines are simply transferred as straight lines.

Can anyone comment on whether this is what one normally sees when transferring drawings to illustrator?