For PVR, MythTV
seems to be the popular choice.
The web browser (and, by extension, youtube) shouldn't differ from Windows. Chrome, Firefox and other big name browsers are available on linux.
For image editing, GIMP is the usual choice. Not sure about video editors. They're out there, I've just never used them.
Regarding PIP: http://ubuntuforums.org/showthread.php?t=1590824