About your requirements, Iceweasel is the supported Firefox derivative (fork), I'm currently running debian as my desktop OS at work and use iceweasel every day, no problem. Gnome3, I think it'll be available on the next stable release, BTW what release are you running? Squeeze? If so I think (IIRC) Wheezy will have it. And finally, about graphics performance/quality, that depends a lot on your graphics card and its driver, but if you think of it like having transparencies, windows closing with fancy effects and so on, you'll need a moderm desktop or compiz (work with gnome2) which I think its available on stable (wheeze).
I have modified a bit your sources.list for wheeze, do you mind to test it and report back?
deb http://http.us.debian.org/debian/ squeeze contrib non-free main
deb-src http://http.us.debian.org/debian/ squeeze main
deb http://security.debian.org/ squeeze/updates main non-free contrib
deb-src http://http.us.debian.org/debian/ squeeze/updates main
# squeeze-updates, previously known as 'volatile'
deb http://mirror.cse.iitk.ac.in/debian/ squeeze-updates main non-free contrib
deb-src http://mirror.cse.iitk.ac.in/debian/ squeeze-updates main non-free contrib
# 3rd party repositories
deb http://packages.dotdeb.org squeeze all
deb-src http://packages.dotdeb.org squeeze all
deb http://www.deb-multimedia.org squeeze main non-free
If you happen to be using wheezy or sid you'll have to change all squeeze ocurrences for the one you're using.
Please, backup your sources.list before replacing it, then test it as follows:
Refresh caches
# apt-get update
Search package
# apt-cache vlc
Install package
# apt-get install <package_name>
If find trouble, please report back with output for those three commands, or at least for the first and last.
Also, if you are already using Wheezy or sid, forget what I said about Gnome3 not being available, it should be there but wheezy is yet to be release and sid is always the development branch.
libc6 : Breaks: libc6:armhf (!= 2.19-19) but 2.19-18+deb8u1 is to be installed
libc6:armhf : Breaks: libc6 (!= 2.19-18+deb8u1) but 2.19-19 is to be installed
One of the rules of Debian multiarch is that versions must match exactly across architectures. Debian jessie has version 2.19-18+deb8u1
but somehow you have ended up with 2.19-19
installed for amd64 (and presumably i386).
How your system got into this state in the first place I do not know. Maybe at some point you or a previous admin changed the sources.list
to testing and then changed it back to jessie.
Downloading 2.19-19 for armhf from snapshot.debian.org and installing it manually with dpkg may be a solution.
http://snapshot.debian.org/archive/debian/20150710T034220Z/pool/main/g/glibc/libc6_2.19-19_armhf.deb
Best Answer
You don't say whether or not you want to end up with Squeeze or Wheezy. I will assume you want the former, in which case you can downgrade to it by giving it a high pin priority:
That way, running
apt-get upgrade && apt-get dist-upgrade
is going to 'upgrade' all installed packages to their Squeeze versions.