tbsmith wrote:
If I back up everything via time machine and then delete files from my HD to free up space, will Time Machine keep these old files?
No it will not, eventually TimeMachine will delete them as TM is a rotating in time backup image of your boot drive, it drops off the old stuff as new stuff comes in and time passes.
If you want to free up space on your boot drive, you need another external powered drive and drag and drop files to it, label it as your extra storage drive.
You can read more about different purposes of drives in my exhaustive thread here
https://discussions.apple.com/thread/3358920
You can read more about TM here
http://pondini.org/OSX/Home.html
If you are trying to make room on your boot drive to install another partition or Bootcamp/Windows, you need to state so now as there is another proceedure you must follow to move all data to one side of the drive to make room for the second partition.
Just because you free up space on the drive doens't mean it's all on one side, it's still spread out all over the drive.