Yep, you got it right.
Hotlinking is when you link directly to an image on someone else's site, or to an image on someone else's image hosting account. What this does is steal their bandwidth.
Any time you want to share an image on any forum, the best practice is save the picture to your own computer, upload it to your own account on the image hosting site of your choice (Photobucket, Tinypic, etc), which is what you've done.
Just a couple of things. Can you please pic three images and remove the IMG tags from the rest, leaving them as links people can click on to see? We ask people to limit themselves to three pictures or less in requests or WCIF to help the page load as quickly as possible for those with slower connections. Also, I merged your posts. If you post and think of something new to say, please click the "modify" button and add to your post instead of replying to yourself. The only exception would be if 24 hours or more had passed since your post.
Thanks!