Ok, this is a quick answer, but hopefully helpful.
I run Mandrake 9.1 at home, so I can tell you what works for me...
For P2P file sharing, I have yet to find a very good searching client, however BitTorrent works very well for downloading files once you have the torrent to download from.
As for browser, I use Opera, and have found that it works great. I am using version 7.11.
For an e-mail client I use the KDE default KMail and I have not had a problem with it, it does everything I need an e-mail client to do.
As for software installations/management, you're in the right place. Mandrake comes with RPMDrake, which you can get to from the Mandrake Control Center. It uses the Red Hat Package Management (RPM) system to install and manage software. The RPM system will automatically check for any dependency problems during installs or uninstalls and let you know what you are missing (for an install) or what you will break (for an uninstall).
To install new software all you need to do is download the *.RPM file for the software and double click on it in Konqueror.
To remove the software you have to open Mandrake Control Center, and select the Software option (IIRC). Then you should have 4 icons, one to install software, one to remove software, one to update software (checks for updates on a mirror) and one to set update sources. Choose the remove option and select what you want to uninstall from the list. Couldn't be easier...
Here are two places where you can find new RPMs: