Video_TS: Do you already have the files decrypted and on your hard drive? If yes, then you can burn them with IMGburn, http://www.imgburn.com/, if not, you will need a program to decrypt the DVD like DVDFab, http://www.dvdfab.com/.
Avi files: You can use Imgburn to burn the files to disk, if you need to convert them to DVD format try DVDFllick, http://www.dvdflick.net/.
Mkv to avi: Try this program, http://www.winnydows.com/page.php?2.
To join avi's: Virtualdub, http://www.virtualdub.org/