There are two major sites that deal with World of Warcraft addons. Curse and WoWInterface (See related links for the addresses). Google code is starting to have more and more addons as well, however, those are a little harder to find.
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Download a wow addon manager like wowmatrix. Google Wowmatrix --- Inside your World of Warcraft game folder you will find a folder called "Interface". Inside is a folder called "Addons". Addons provided on abovementioned websites usually come zipped, with the files in a folder with the addon's name. Simply copy this folder entirely into the "Addons" folder. Make sure to quit WoW and restart it. At your character selection screen, at the bottom right, is a button "Addons". Click it to see a list of addons you are using. Make sure all addons you want to use have a tick in the box, and that the box "Load out of Date Addons" is ticked, in case you installed an older addon. Log into your character, and the addon should now be active.
Yes, you can use any addons that a full account can use. There is no limit.
Yes, the Curse website (and Curse Client) is safe to download addons with. However, like all other sites that have ads (advertisements), you can be infected with viruses from the technology that is used for the ads (specially flash ads). This is mostly true for any site that has ads, Yahoo, MSN, MMO-Champion, and others.
Considering WoTLK is 18 GB Normal, i'd keep atleast 25 - 30 gb for catacylsm inclusive of addons
Wow takes about 2-4 hours to download but it will be worth it when you start to play