What kind of line did you buy and where?! They should have put it on for you...
Yes you should put on backing! Depending on the type of reel you have (regular arbor or large arbor) and the type of fishing you will be doing (trout or pike) you should have about 250 yards of 20 lb or 30 lb dacron respecfully).
Yes line is tapered! The "running line" is thinner then the body/head
Think of it this way (approx):
Typical profile for a WF (Wieght Forward line):
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70 feet 20 feet 10 ft
Typical profile for a DT (Double Taper line):
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20 feet 60feet 20 feet
See here for an exact WF line profile (click line profile box):
http://www.rioproducts.com/fly-lines...io_perception/
And for DT:
http://www.rioproducts.com/fly-lines...ream-trout-dt/