Back up cartridge/retail versions of 3DS games

There will be no 3D effect with a regular DS game, as this IGN article states:

Standard DS games will not have the ability to be displayed in stereoscopic 3D on the 3DS. DS games will...only be displayed in standard 2D.

To further the point, on this comparison chart from Nintendo, it states at the bottom that:

Only Nintendo 3DS software can be played in 3D. Nintendo DS and DSiWare software will be displayed in 2D on a Nintendo 3DS system.

The only way you will be able to play Mario Kart in 3D is to wait for Mario Kart 7 to be released in December.

Short Answers

1. Yes
2. Yes
3. No

A bit more detail

1. Since the 3DS doesn't have a whole lot of built in storage, some sort of flash cart is going to be necessary. This likely remains true even if there is, or comes to be some sort of lasting hack that would let you run homebrew from the SD card slot.

2. Most flash cartridges store the bulk of their data on an SD card(usually Micro nowadays) that you provide, thus practically requiring an SD card.

3. To the best of my knowledge, the business of flashing the DS itself is an old practice. Before the system had been so thoroughly hacked, flashing was one of the favorable options. Downsides included the fact that it would technically void your warranty(but wasn't really easy to detect). Basically, you could flash your DS, but all of the up-to-date carts will achieve the same end result without changing anything on the actual DS.