Q: If you have armor and weapons on you person that are no longer available in the game can you use those skins?
A: Yes, you can -- assuming they fulfill the other criteria for eligibility.

Q: If I have a weapon that equips on the hip and I mog it to one that equips on the back, will it continue to equip on the hip (like the original) or will it switch to the back (like the one I used to mog with)?
A: The way a weapon sheathes is tied to its artwork, so the weapon will appear sheathed in whatever fashion the source item for Transmogrification did. (Blue Tracker / Official Forums)

Q: Will Main Hand only weaponry be 'Mog"ifiable to the offhand slot?
A: Mainhand can only be applied to mainhand, and offhand can only be applied to offhand. This is partially due to the restrictions on certain types of weapon art.

Again, these are our first tentative steps with Transmogrification, and there's room for modifying the rules later on after the system is introduced, and we see how things shake out. Heck, the rules aren't even quite set in stone right now, and might change further before the system is introduced.

Q: If WoW was designed to not be "silly" why have the items in the game in the first place?
A: World of Warcraft has a design aesthetic that limits silliness, not omits it utterly. We all like a laugh now and then. That's why we have so many fun novelty items, easter eggs and humorous quests. Still, with a handful of exceptions, there's been a pretty firm line drawn between what amounts to a novelty item (which we anticipate players showing off occasionally for a laugh, or to enjoy on a temporary basis), and items that we intend players to use in their day to day activities.

It's that handful of exceptions that are the sticking point. It's the items like frying pans, cleavers and rolling pins that we're not sure we want players running around with on a constant basis. The jury is still out on that.

I'm sure that there will be those that still find ways to make the most ridiculous outfits possible despite any precautions we take. We can't possibly anticipate every permutation of gear combinations that people will come up with, but we can strive to design the system so that there are fewer completely ridiculous looking characters running around. Yes, that's partially subjective. Yes, we also have a design aesthetic that, even with the introduction of the Transmogrifier, we still want to adhere to. No, I don't care if you personally think that any given tier set looks "silly"; that's not what's at issue.

(...)I'd like to provide an update on this statement I made. It turns out that Heirlooms will be eligible targets for Transmogrification. Also (and this applies to all Transmogrified items), trading, mailing, auctioning or depositing an item in a guild bank will remove the Transmogrified art, returning the item in question to its original artwork. So, while you won't have to stare at the same old Heirlooms the whole time you're leveling, you won't be able to send a set of Heirlooms that have been Transmogrified with tier 13 art to your level 10 alt.

(...)Mainhand can only be applied to mainhand, and offhand can only be applied to offhand. This is partially due to the restrictions on certain types of weapon art.

Again, these are our first tentative steps with Transmogrification, and there's room for modifying the rules later on after the system is introduced, and we see how things shake out. Heck, the rules aren't even quite set in stone right now, and might change further before the system is introduced.

(...) The gear also still has to have stats aside from armor on it. That means that there are a lot of white or grey items that might not be available initially when Transmogrification goes live.

As an aside, a lot of people have been asking about hiding shoulders, belts, etc. For now, it's looking pretty unlikely that we'll offer the option to hide anything aside from helm and cloak.

We're still discussing exactly what will or won't be available for transmogrification. So far, as others here have said, if it has stats and isn't a "silly" item such as a fish weapon, to my knowledge it will likely be available to transmogrify. However, as I said, nothing is finalised yet and things are subject to change before and after the feature has been released.

(...) The Transmogrify feature will allow players to customise the look of their character within reason. We've already stated that it's likely certain items will not be available to transmogrify, including fish as weapons, and other items such as frying pans, for this very reason. As you know, armour types will also be locked, preventing tanks in cloth dresses for example.

The rules will be tweaked as time goes on, but we're keen to keep the outlandish outfits to a minimum. What players wear while socialising in cities is up to them, exactly the same as now.

The gold cost for Transmogrification hasn't been set in stone, but it's likely to be very similar to Reforging, meaning it'd scale with item level (probably the level of the item actually equipped).