Thanks for the suggestion. The instructions for preventing items from starting at boot didn't work for me, as iCal was not listed as one of the items. Maybe it's somewhere else, such as how to control the dock. It's strange that this only started happened AFTER I removed the cache. No idea what prompted iCal to activate itself.
I don't have access to a Lion system, but go to iCal on the Dock, and right click. Check if the "Options" on iCal show "Open at Login":
If so, uncheck that option.
On another note, when you shut down, iCal, and any other open Application will reopen automatically, unless you actively make a choice not to automatically open Applications when shutting down your computer. You can also quit iCal before shutting down.
Ah, that seems to have worked. I also had issues with items on my calendar I thought weren't syncing to my iPad Air, but then I discovered that I have two calendars (not sure how that happened--may have been that iCloud created a default calendar for me that wasn't my iCal calendar, and I just never noticed), and that on my iPad one of the calendars wasn't selected. I wonder if there's some way to merge the calendars and leave only one to deal with (because some events are showing up *three* times now in some places). If not, I'll manually move items and delete one of the calendars.
I also now see that iCal appears on the dock after I open the iCloud Calendar. When I upgrade to 10.9, will this duplicate program go away (hopefully)?