Just loaded up the file, looks like some parts aren't loading in right for me. This is what I see...
Anyway, I notice that you're using bevel gears with the worm gear - I don't think that will work right. With the spacing you have there, a "12 tooth double bevel" gear may work.
You may have realized this, but Studio hides parts that aren't available in the color you have selected. To get around this, uncheck "hide unavailable colors" in the color menu - I just thought you may not have been able to find the right gear you were looking for in the menu because it was hidden.
About the axles, you probably want to buy 6 long axles and cut them to length to get them just right. I suggest using a file to smooth off the ends after cutting, they'll be jagged if they are just cut and left alone. Besides - black 5 long axles are pretty expensive.