Welcome to Azeroth /wave
You'll gain more spells and abilities automatically as you level up, and once you reach level 10 you can choose a Talent Spec that'll include extra abilities. For warlocks your choices are Demonology (focuses on working with your minions), Affliction (focuses on more Damage over Time (DoT) combat), and Destruction (focuses more on big badda-booms), and each will have LOTS of buttons to push by the time you reach level cap.
Right now only the Hunter class can use bows, so all you can do is sell it to a vendor. Sometimes you might find one that has extra stats on it like Agility, and in that case you can try selling it in the Auction House (AH) in case another player might want it. And all you do with your staff is equip it, although if something gets too close to you you'll probably bonk it on the head automatically -- later you'll start to find weapons that have Intellect and other useful stats on them, and that'll be the only reason to equip them. For casters, staves and other held weapons are considered "stat sticks."
You can choose any professions you want, but if you plan to craft things with one, it's helpful to pick up the matching gathering professions; for instance, Herbalism provides the herbs needed for Alchemy. Tailoring and Enchanting pair well, since you use the cloth found as drops to make items, then disenchant them for the materials (mats) used for leveling Enchanting. However, for brand new characters it can be very beneficial to take two of the gathering professions (Herbalism, Mining, Skinning), and sell everything you gather in the AH. That way you can build up some gold to use for mounts and training, bags, funding alts, and leveling a crafting profession.
You can learn all of the secondary professions (Cooking, First Aid, Fishing, Archaeology), but the first three have more direct benefits, Arch is more for fun and occasionally finding something useful. Cooking's good because later in the game you can make foods that provide buffs, and First Aid can be handy for a quick heal now and then, although many have noticed it's less necessary these days.