I installed three add-ons for 2010. Can I go back and remove those?
Not automatically, unless you used an external mod installer tool. Manually only if you know exactly which files were added, replaced or modified by the addon, and if you can reverse all these changes. This isn't trivial as you found out, so a fresh install is a safer option.
What about add-ons intended for earlier versions of Orbiter? Would add-ons intended for 2006 work in 2010?