Here's the manual from an '08, it's the same for the '09
http://www.zggtr.org/index.php?action=dlattach;topic=1528.0;attach=2110You can ride just fine without the feeler on the bottom of the peg.
For the battery, yes, the right side. There are two access panels that have to be removed. The first is plastic, it only has one bolt to remove but there's a snap in connector holding it in after you get the bolt out. The snap connector is behind the lower right corner, get your finger tips under that area and pull straight out.
The second panel is metal and once you get the plastic panel off you'll see the whole thing. Be VERY careful removing the bolts on this thing. LOTS of guys have stripped the heads of the bolts since they seem to be made from chocolate. Once you get this panel off you should be looking at the battery. The positive terminal should be facing out. Some dealers installed the battery backwards, it's possible since the battery wires are long enough.