most video players like vlc will play music and video but not pictures
the file manager shows thumbnails for movies and pictures which you can enlarge to pretty much any size you want and the new gnome file manager (nautilus allows an extra pane - F3 - so you can view two directories or files at once) (btw you will have to remove the movie or pictures from their respective folders into the parent folder if you wish to see the preview thumbnails together. This could be messy so 2 panes helps)
Also you can preview a song by hovering above the file with your mouse pointer.
Konqueror, the KDE file manager, was trying to do what you are suggesting but I use gnome so I don't know how far they got. Okay so I installed konqueror and it does integrate web browsing If you decide on KDE DO NOT REMOVE GNOME UNTIL YOU HAVE A FULLY FUNCTIONING KDE SETUP as you may not be able to login if it is not fully installed!! Log out of gnome and into KDE before removing gnome. Try KDE for a while is my first advice but I wanted to warn you as I switched to KDE once and didn't try it before removing gnome in the same synaptic session! I had to finish up with a live CD.
Other than that there is the web browser which will be able to all of this soon but can do it now by visiting sites. Including video and picture editing etc
Songbird for windows or Firefox for both but the best I have found so far is . . . . . . .
Dolphin for gnome - I tried it and it is definitely better than konqueror for the features you asked about and this has rudimentary controls for the music and video with a split screen (extra pane) for easier file management via drag and drop instead of cut and paste though konqueror has web browsing and should have done better from memory so maybe the plugins aren't working with my gnome setup (mixing gnome and KDE always messes something up and I haven't had them both for a long while - Mandriva was the best for having both desktops working well together (remember KDE uses more resources too)
You can open a video, music or picture file in firefox but there are no controls. You can use it to view your files and folders with support for reading and saving pdf files (sudo apt-get install acroread) Get the vlc plugins for firefox too (and vlc is the best video player btw - it does things like moving the audio track slightly forwards or backwards when the voices aren't synced correctly, ditto with subtitles and has a hundred other features; several hundred if you include the command line!)
Dolphin and Firefox (with plugins). Opera and Chrome's extensions were poor but they are getting better. Gnome-do is fantastic once you have learned it as it can open any file in a flash!