The process required to transfer virtual console games from the Wii to the Wii U

No, it does not.

Nintendo currently only sells a small fraction of the Virtual Console titles on the Wii U as they are converted to Wii U for controller compatibility and other reasons.

You can still purchase these games on the Wii U from within the Wii virtual machine environment via the Shop Channel and Nintendo is still distributing games for the Wii through this shop (including some of it's Club Nintendo giveaways).

It is very unlikely that many if not most of these games will ever be ported for native Wii U play due to the radical change in controller schemes. All Wii U games are required to support the tablet as the primary controller.

As for the second part of your question, the only significant game I am aware of that will not transfer to the Wii U's Wii emulator is Lost Winds. I have also found anecdotal evidence that DLC for Final Fantasy The After Years fails to transfer as well and neither can be downloaded from the Wii Shop Channel on Wii U.

One added note as this was touched on in comments. Nintendo has indicated they will re-issue an unspecified number of Virtual Console games on Wii U and if you have already purchased the Wii version and it is linked to the Nintendo account you transferred from a Wii to the Wii U, then the new release will be offered to you at a greatly discounted prices ranging between $0.50 to $1.50 in the U.S. (if you did not transfer your Wii profile to your Wii U then you are not eligible for the discount).

Correction: In April 2014, Lost Winds became transferable from the Wii to the Wii U. To transfer it you will need to have held onto your old Wii system and repeat the transfer process. Otherwise you'll need to repurchase it.

Unfortunately, that's impossible. About as impossible as transferring a Mii from a 3DS to a Wii is.

The reason for this, is that 3DS and Wii U Miis have features that do not exist on the Wii, such as additional hairstyles.

According to Joystiq:

But what if you want to send a Mii back to the Wii? "It's a one way transfer," NOA Product Marketing Manager Bill Trinen told Joystiq. "You can send your Miis from your Wii to your 3DS. But, because the Mii Maker on the Nintendo 3DS is a more robust program and has newer features, like hairstyles and eyes and things like that, the Miis you create there can't go back to the Wii."

The same holds for the Wii U as well.

Unless Nintendo updates the Wii's Mii channel to add those features, there won't be any way to transfer Miis back to the Wii. Since the Wii has been replaced by the Wii U, such an update most likely won't see the day either.