You have 3 or 4 rather complex questions that each require a bit of explaining to answer. I can't answer each adequately in this format. I can answer them inadequately though.
How does Time Machine work? It's a feature on your Apple OS machine that backs up your entire machine. If you click on it you can essentially go back in time and see your computer fro any backup. So you can go into LR from a previous backup and use it as if it was that date. It's COMPLETELY independent of any LR feature.
How big of a backup drive should you get? It depends on how many backups you want and how much hard drive space you are using. It doesn't depend on how many pictures you take. I recommend a backup hard drive for Time Machine that is 3-4 times larger then the size of your used hard drive.
Is it backing up a new file every knob i make in LR? No. That's the exact opposite of how LR works, and why its' so great. LR does not touch the original file. It only write to a text file that tells LR how to form a preview.
How does the history feature work? Part of the LR file (called the catalog) saves every change you make to a text file. The history feature lets you see those changes. Since it's just a text file, it can save all the changes you ever made. You can't copy over previous changes. It just records all the changes you've made. (Photoshop works completely differently BTW.)