If you can see the tracks in Exporer, then you should be able to copy past into Reaper. You will see a message I think, separate tracks or consolidate, something like that. This could be the case it is so easy ... But it should be that easy.
I recently picked up a DP-008EX and in a discussion with someone with the 008, he complained that while he could do this, the tracks are exported in some Tascam proprietary format, which was a nuisance to convert.
I have no idea if this is true. The DP-008EX exports in .WAV format, though.
Yes. Use the EXPORT function on the DP003 (will create WAV files ... must be 16bit 44.1 kHz). Attach to the computer via USB, copy the WAVs to the computer, in Reaper chose Insert|Media File and open the file(s) in new tracks. To go back, be sure you are working in 16/44.1 format WAV, no other file types or resolutions are acceptable.
You'd still have to convert the internal, proprietary Tascam format before you'd have WAVs ready for the DAW. The actual USB transfer is no problem. I prefer to use USB ... no physical wear and tear on the cards or the card readers.