Can a 3DS receive DS Download Play games from DS cartridges

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.

The short answer is no, you can't transfer individual eShop games.

From Nintendo's 3DS General Information page:

Can the downloadable version of a Nintendo 3DS game be transferred to another 3DS console?

It is not possible to transfer a specific software title to another Nintendo 3DS console. However, it is possible to perform a System Transfer and transfer the entire content of your console to another. For more information please refer to the System Transfer section of this Website.

I had to dig a bit to find this information, it is under 'Nintendo eShop Information -> Downloadable Retail Software - Frequently Asked Questions'. Also keep in mind this tidbit regarding System Transfer, under 'Transferring Games':

How Many Times Can I Transfer Content from One System to Another?

Data can be transferred up to five times. A system cannot perform a system transfer multiple times within a set period.