Hey Woalgone - welcome to Everquest.
First of all, the Mage is indeed the character class that can summon weapons, armor, arrows, magic items, and a ton of other great stuff for both pets as well as other characters. The usefulness of mage summoned gear (for player characters) has dropped off a bit over the years compared to the defiant gear now in use, but mage "pet toys" (summoned items optimized for pets) is something no other class can do, and always in great demand.
As far as getting spells, you have to keep in mind that Everquest has grown so large in size that it's no longer really practical to click on every merchant to try to find spells - this game is just gigantic. So, you will want to use allakhazam to locate all your spells you get for the next few levels. I usually write these spells down on an index card, along with what merchant sells them, and whether they are player-crafted.
Buying your spells require you to go to a merchant that sells the spell (obviously). However, even most mage spell-merchants will likely not have the particular spell you are looking for. This is why it's important to know ahead of time what merchant sells the spell you want - just use this site to find out who sells it. You can try to buy all your lower level spells from the spell merchants in the Plane of Knowledge, but spells that can be used by several different classes ("common" spells) may be sold by the last merchant you would expect - so look up who sells it beforehand - seeing a pattern here?
Eventually, you'll probably have to research your own spells - that's another topic for another day, but basically you will buy a spell research kit, and combine several special components to make the spell. You have to have a lot of skill points to make the better spells though, but it's a great way to make money if you're good enough.
A raid is when several groups combine together, generally for the purpose of taking down a boss mob that a single group cannot. A raid can have a huge number of characters in it - over 50 - it's one of the great strengths of Everquest (many say). Normally, you will be raiding with other guild members, and it's (for the most part) an end-game activity. For some folks, raiding is everything; for others, it's just not their preferred style of play. Folks usually raid to get special, rare items you can get nowhere else, though sometimes, raids are done to get people keyed or flagged to enter certain zones that were "locked" to them previously. In general, only experienced, high-level characters will be invited to raids - it's not usually something casual players do.
I hope this answered your questions.
Edited, Aug 19th 2009 1:38am by zirumkin
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If you can't do something well, learn to enjoy doing it poorly.
My Rathe / Prexus characters:
Bigbronze Bloodyaxe, 62 Ogre Berserker
Verbeeg Bearfang, 62 Ogre Beastlord
Glabrezu Spiritcaller, 62 Ogre Shaman
Zirumkin Zenomorph, 62 Gnome Wizard
Korgulon Soulwraith, 76 Ogre Shadowknight <Shining Alliance>
Incarnadine Summoner, 65 Drakkin Magician
Bristlebane characters:
Zalkahriz Ebonscale, 64 Iksar Necromancer
Gnomorre Gniceguy, 55 Gnome Rogue
Whytfire Lonewolf, 55 Woodelf Ranger