During installation I was asked to remove my DivX, because it is embedded into K-Lite Codec Pack. Is DivX legally used with K-Lite, or is it a pirated compilation?
Yes, it's legal and you can use it. You shouldn't uninstall DivX because there are no legal issues. The codecs used in the K-Lite Codec Pack are third party which means they can be used to play DivX encoded files. You should re-install the codec as needed without removing the pack. I advise using the FULL version of the codec to enjoy all the features and programs that are built-in.
Download page: http://www.codecguide.com/download_k-lite_codec_pack_full.htm