See below in the related links for a map to the Goblin riding trainer, Revi Ramrod.
Depends on whether you are Horde or Alliance - Alliance learn them from their trainer in the Slaughtered Lamb in Stormwind or you can get an imp in Northshire after the quest 'The Stolen Tomb', or in the 'bad area' of Iron Forge. Horde, the trainer in Undercity or Ogrimaar.
The Undercity is the capital city for the Undead. It is built under the ruins of Lorderan.
work with it for about a month ,lounging it ,riding it. or send it to a trainer
There are a lot of dudes that are in UnderCity, if you're talking about a guard or something, they can't talk, their controlled by the computer, called NPC.
To get the training you need to ride a basic mount in World of Warcraft, simply go to any riding trainer and they will teach it to you. To use a races mounts however, you need to be exalted with that race, except if you are that race. Some classes automatically get their first level of riding when they purchase their mount spell from their class trainer. Warlocks and paladins get their training from their trainer at level 20, and Death Knights are always made with level 40 riding already learned.
equine vet, horse trainer, horse breeder, riding judge (showing), riding instructer, professional rider :)
A cycle trainer is someone that helps an individual learn, and perfect bicycle riding for those that are planning a bike competition or bike marathon.
an hour
The riding trainer is in a building that is outside of Silvermoon a little north west of the gate. EDIT: If you are looking at the Map (hit "M"), the stables are SE from the gate, make a straight line down from the "V" in "Silvermoon" on the map and it points right to it.
As a Mage you can teleport to major cities. You should have the spell to teleport to Stormwind or Undercity (I'm not sure about UC as I play Alliance.) and there is a trainer there. Or are you asking where to level your Mage? If so, Horde or Alliance? PVP or PVE Server?
Yes. If you don't have it you could be majorly screwed if there was an accident and you were held responsible.