I see the option to add a bounty to other poster's questions, but not to my own. By design? Am I missing something?
Sorry if this is covered elsewhere. I did look.
Sure, your questions are no different from anyone else's for the purpose of bounty.
Pay very very close attention to the rules at the bottom of that section!
(also note that any bounties you have offered now or in the past are on the bounty tab on your user page.)