TM performs a backup of 120GB of files and one of them is a photo of my childrens first day of school; then three weeks later there's another backup that has a new video of the kids at a hockey game, but to make room for my almost full HD on my MacBook, I delete the photo of the first day of school
That is not a good idea at all! TM will probably not delete that photo from the backups right away, but it will eventually.
You need to have more storage space - either another external drive, or a larger internal drive - so you don't have to delete photos to make room for more stuff. You also need to make sure that everything you put on any external drives gets backed up somewhere else.
Because I made backups to the DVDs, I deleted those files from my MacBook to make room thinking I was safe. Now there's files mixed in the TM backups that I want but don't know where they are.
That's a pretty significant problem. I don't know whether the stuff you put on those DVDs is any good or not. TM backups are complex, and are not just normal files and folders. So you may already be missing data that you were relying on that backup system to preserve, and even if the DVDs are good, you'll still have a lot of work manually digging through all of them to look for files that have been deleted from the TM backup.
As for examining the TM backups themselves, there are some tools for doing that sort of thing. See:
http://pondini.org/TM/A2.html