I'll try to be complete and understable, but english is not my mother-tongue and I just woke up lol, so forgive me :D
1)
First I'll try to explain about repositories. There are several repositories, or mirrors if you prefer. It's a database of packages on a server. Packages are compiled softwares, maintained by the packagers. It's the same, more or less, for every distribution, not only Fedora. The packager pick the source or build it, then he makes a package, which is the software, compiled for Fedora, that you have with Yum.
The graphical tool, I think that in english his name in the "menu" is "Add/Remove Software", can be worth if you know what you search. But, yes, Terminal is, imho, way more useful, but maybe it's because I know what to do with it. Don't hesitate to look at the documentations, and there are a lot of websites explaining everything, a bit like the books "... for dummies" :p
There are some websites that are letting you explore the repos, like pkgs.org, or an official Fedora one but I forget his name/url...
Bonus : you can search alternatives to Windows apps here.
About what cp702 said : "you can download actual package files from, say, a website, and install them directly", it's true, but it's often not recommended, because of security and conflict issues that may happen. Of course sometimes it works without a problem. Just be advised that it can provide issues. Try to always use official or trusted repositories.
If a package is old, use Bohdi website to make a ticket or request.
2)
Gparted is free and well-reputed, don't worry about that.
About commands, as I said, read some documentations, for end-users the commands to remember are just a few, and they are more-or-less the same for every distro.
And about su/sudo, in Fedora sudo isn't well configured by default, but anyway I don't like it, because of its behavior, I see Sudo as a security hole for non-experimented users.
About RPMfusion, you'll have to install the codecs from that repo, just installing the repo won't help ^^
Default GNOME Fedora provides Rhythmbox, it's a bit like iTunes (a bit). You have Audacious, Clementine, etc... there are a lot of tools. And you have the excellent Amarok, but it's a KDE component.
3)
Uninstalling software :
- graphical tool : go to the section which display your installed softwares (or maybe a filter to tick, sorry I use some different specific tools or terminal).
- terminal : su -c yum remove packagename
You can look at this : http://fedoraproject.org/wiki/User_Guide_-_Managing_Software
4)
Pepper is directly integrated in Chrome (but only Chrome, it's a Google+Adobe "product").
5)
As cp702 said, GNU/Linux distros are less energy-hungry than Windows, but I was talking about GPU, sometimes without proprietary driver the GPU can be always running at 100% with a nice big fan noise and an increased electricity consumption.
---
To conclude, I like Fedora for some reasons : fresh up-to-date packages, flexibility, "philosophy" behind it. Ubuntu is great for beginners, but Fedora is not that complicated, it just needs a bit of learning.
Test several distros (VirtualBox may help ^^) and use what you like ! And don't care about distros flamewars, trolls don't help.