How can I switch to Linux if I need to use these apps?

Cut/Paste/Move Video Sequences take a look at Kino

Also supposedly the CVS version of Cinelerra aint bad, but unfortunatly I havent had good luck with it. You are right though, there doesnt seem to be a good video editor that I have found, though you can give this one a shot...

http://www.jahshaka.org/

Ive takena look at it a few times but never tried it so I cant speak anything for how good it is. At the moment I still go to my Mac for FCP when I need to do video editing.

In as far as Gimp, as long as you are not doing Print images I can do most things in Gimp that I can do in Photoshop. Its real shortcoming is CMYK which is why I wouldnt reccomend it for serious print work, but for digital images I find it fine. On the Mac I use GimpShop which is nothing more than a patched version of Gimp to replecate some of the key commands and menus to be closer to photoshop. I believe there is a version for linux as well, it tends to be slightly behind the released version of Gimp as it is just one person patching it, but overall it is pretty good. Or if you prefer to stick with the full version of gimp and tackle a learning curve that is obviously an option as well.

In as far as running video editors via emulation... your speed will go downhill. It can definitly be done via Parallels or VMWare, but it will mean taking longer to render etc.

Seablade

You can also try Cinelerra:

http://heroinewarrior.com/cinelerra.php3

or kino:
http://www.kinodv.org/

and Main Actor (although it is pay software, they have a demo):
http://www.mainconcept.com/site/?id=954

Cinelerra is very complex. Beyond my needs or abilities, but if you have professional experience, it may be just what you are looking for. Also it requires a rather beefy box. They recommend dual Opterons, 64 bit, and 4 GB of PC3200 registered memory.

EDIT: Forgot to mention some other nice graphics software, xara:
http://www.xaraxtreme.org/

and scribus:
http://www.scribus.net/

While Gimp is a pretty awesome package and well supported, it's probably the only app that you will find in the Linux world that can be an outright replacement for something in the Windows world, as in Photoshop that you mentioned.

In terms of video editing and dvd authoring, it's going to take a lot of work to find a good solution for you under linux. (It's even worse for a Mac user in my opinion because of the good work Apple did integrating iMovie and iDVD for the inexperienced videographer) Here's my starting points;

http://www.exploits.org/v4l/

Is a good place to start getting some information on Linux video editing packages. But there are a couple that I've looked at that are not on this list, they include;

Diva
http://www.diva-project.org/

PITIVI
http://pitivi.sourceforge.net/

and as mentioned already Jahshaka
http://www.jahshaka.org/

As far as DVD authoring you can start doing some research in the following places;

A good Linux Journal article/Howto on DVD Authoring under Linux
http://www.linuxjournal.com/article/6953

Another user's Howto
http://gecius.de/linux/dvd.html

This is a slideshow presentation on how the author of Linux Multimedia Hacks sees DVD authoring under Linux (maybe not as useful as the previous Howtos)
http://www.greenfly.org/talks/multimedia/dvd.html

(when the first page opens you need to click your mouse to advance the slides)

A Gentoo wiki on DVD Authoring
http://gentoo-wiki.com/HOWTO_Create_a_DVD

And finally a long Slashdot thread ramble on the subject..
http://ask.slashdot.org/askslashdot/.../0115229.shtml

In the end I would have to admit that it would be easier to use a platform like the Mac or even Windows for immediately coming up to speed on this stuff. There's a lot of support out there for those platforms. But the power and flexibility that you get by going to Linux is much greater. (There is a reason why some Hollywood movies are being edited on Linux platforms) There's unfortunately a bit of work involved.

Wow that statement is so wrong(No offense to you intended, seen several good posts by you recently.... Actually video editing is one of the few areas where there might not be something to use as a replacement, gaming being another one obviously Buisness you have several solutions ranging from open office to various money suites etc. And my personal experience is with Audio where I can list off more software packages as replacements for Win/Mac software than I care to at the moment In fact Gimp is a worse substitute for Photoshop than many of those audio apps are to their counterparts as Photoshop most often gets used for CMYK professionally, which means Gimp cant keep up. Seablade