I want to restore files from Time Machine without restoring applications and Library files. Can I just open up my time machine backup folder on my external drive and manually drag files to my desktop for only those files that I need?
When you drag files from an external drive in OS X it just copies (not move) the files, so if you just dragged some files out you did not hurt the YM backup.
The issue is sometimes what you are dragging out if not the actual file but hard links to the file. Read the section here on hard links. So sometimes you can drag out a file and just get the link and the file won't work. If the files you dragged out are working okay, you are fine.