I have to correct about 200 files in Elements and once I have them corrected, is there a way to batch save all of them to one folder?
I suppose you don't open your 200 files at the same time in the editor to correct them? Generally once a file is edited, you 'save' or 'save as' and close the file.
If you have saved each file after editing, the 'batch' savjng to a new folder is a very simple operation from the organizer. Once you have selected (highlighted) all your thumbnails you use the menu File > export to new files. You can choose the destination folder, but also the size, the format and even rename your files.
As a matter of fact, if you have just edited a batch of files without saving them, there is no way to batch save them. That's because each file requires individual 'save as' settings. By the way, I don't imagine you'll have 200 files opened in the photo bin of the editor at the same time, waiting for saving.
So, you have to save your files individually after the edit. The final batch export from the organizer will deal with the destination folder, format, size, quality, etc.
Or are you editing your photos in the ACR plugin?