Your files stop at 2GB because your hard drive is in FAT32 format, and not NTFS. NTFS lets you have extremly large file sizes (the limit for Windows I think is 4TB but don't quote me on that) and allow you to keep an entire show in 1 AVI file. I don't know what version of Windows you are using but the following link from Microsoft should tell you how to convert your drive.
Convert FAT32 to NTFS
Yup, true. Sometimes your capture app will split the files anyway (at a point of your choosing) just to keep the files more manageable. So, you might actually have NTFS, but that cap app will still chop them up. So, you might want to check your preferences. DV is about 13 gigs per hour, so welcome to the wonderful world of video -- and you thought audio was a PITA. LOL!
But seriously, a lot of times, this type of thing would be done in a non-linear video editor. You'd just line up everything, and then encode/render out to MPEG2. I'm guessing the capture app is making perfectly gapless splits. So, you just need to line them up, and encode. There are free tools like mentioned, but depending on exactly what you are doing (you didn't totally say), you might be better off working in an NLE.