Spark when connecting battery
 

Bought a new battery for the wife's o5 sporty, when connecting the positive I get a small spark and the speedometer jumps, has the factory alarm. How much load is acceptable?
The bike had been starting slow, found the lead melting off the battery post, that why I bought a new battery. Never had a dead battery till I got a new one.
After the hour ride I had 12.77 volts, so I know it's charging.

If you have no additional accessories other than the stock and the security system, then I would check the charging system. Run through the VR and Stator checks in the stickies of this forum and see what you get. Melted terminals indicate too much current going either direction to or from the battery. You should be getting around 14V at 2K RPM, anything outside of that will indicate a charging system issue. Too much voltage can cause the lead terminals to melt as well.

And to answer your initial question, if I am not mistaken the Sportster lineup comes with a 35A charging system standard, the usages for the basics aren't very well documented so finding that info can be a chore. That 35A charging system is good for a few accessories but you would need to look at the load specs to see if you are exceeding it. Usually if you are exceeding the load specs of the charging system it will run the battery down while riding.