Should I dual-boot on a second drive?

It's definitely worth asking yourself if you genuinely need to run two totally independent operating systems. The extra hassle that comes from it can be pretty significant, forcing you to duplicate programs or carry multiple versions of a file to ensure that you can open it in both OSes and it just adds time and effort to things that otherwise should be simple.

I agree with Fyrye that visualization is almost certainly a better approach. Personally I would advise that you go the other way around though - Run windows as the main OS and run a virtual linux as needed.

Part of that is because I've seen far too many people get all excited about Linux and then get bored and/or frustrated within a few weeks, so I wouldn't advise anyone to make the jump unless they are extremely certain that's what they want to do. I would definitely not advise any linux platform for video editing. Yes, there are editing packages these days and even pretty good ones, but it's just not the same as working in FinalCut or Avid or even Vegas or Premier. Learning the interface of these applications if a solid 75% of what makes you good at using them; knowing where to find the exact tool you need to achieve some obscure effect quickly and effectively instead of trial and error for an afternoon. I don't know if that's really important to you but you should think hard about it before taking the plunge. If you want to work on anything more than the most casual, least complex basis you should stick to windows or OSX. I work for a small video production company in London, I meet lots of editors and I've never met a pro who works in Linux.

An additional reason to run Windows (or OSX) base is that Linux distros are radically smaller than a Windows install, and the applications running in them are likely to be a lot less demanding so you'll likely get much better performance from both sides that way. It also gives you the freedom to change builds/distros on a whim depending on exactly you are working on at the time while still having your down time apps (games and skype and such) available all the time so you can just drop out and relax some without hassle.

As for actually running the dual boot thing -

Running on one disk will be tricky in this day and age. Windows is kinda possessive when it comes to partitions and I believe by default it will steal a whole drive. Off the top of my head I think it would probably be wise to use a third party partitioning tool to split the drive into partitions, then format one with NTFS, the other with your Linux FS of choice. Then run the windows install and point it to the right partition, and make sure to double check everything to ensure it's not going to just eat the whole disk. Then do the ubuntu install. Ubuntu almost certainly comes with a bootloader, but if not you can find one easily enough (I like GRUB). In practice what will happen when you boot up is you'll get a prompt to pick which OS to boot from.

As for the second question: Unless you are absolutely crazy your linux partition won't be filling up. You might have large files like videos that take up space, but those can be read from any drive that the OS can see. The applications are generally small and the OS isn't clogged with non-essentials the way windows is. If you leave say 30GB for Linux when you partition you should be able to do damn near anything you want to. Linux keeps it's binaries (programs) in /bin and I don't think you can move them. However, windows can install wherever you point the installer so to ensure you have space (especially for games and media files) just format a new HDD into NTFS, point windows installers at E instead of C, and keep your big media files on it too. Both OS should be able to see them. Might not be able to read them without extra programs, but they will be there and available.