How do I remove Buell 1125r battery? Can see it, charge it and loosen the retaining strap by removing the rear seat, but the battery cannot be lifted through this opening.

SOURCE: seat removal 2006 hd flstc got screws loose-but just spring load

If ths is a 1 piece seat ; are all 3 screws loose? If so you may need to pry easily under one of the front 2 screws to get it off

SOURCE: how to remove seat to get at battery

from what i remember on mine, it did have to come off and what a bear it was to get the seat bolts to align properly during reinstallation.

remove the seat, remove the battery, install the new battery (but install a battery tender pigtail and route it down the side), install the seat (lightly tape the hex bolts to the hex wrench so you can stick them in the blind hole) and secure the pigtail to the frame. now when the battery gets low, the seat doesn't have to be removed to top charge it.

SOURCE: buell 1125r cooling system bottle?

The Expansion tank is under the rh radiator pod, need to undo at least 6 bolts to get cover off to access the bottle and to top up the antifreeze

SOURCE: Do not know how to remove the buell seat to get to battery

 THERES A LEVER UNDER THE TAIL END  PULL TOWARDS THE CLUTCH SIDE OF THE BIKE AND LIFT UP ON THE BACK OF THE SEAT AT THE SAME TIME AND BAMM ITS OFF HAPPY RIDING 

SOURCE: how to change a rear tire on a 1125r buell

May I suggest a trip to your local library. Cycle repair books should be in 646 stacks of reference.