1. Yes, DB do send BahnCards abroad (you have to order and buy the temporary BahnCard first and then a permanent BahnCard with a number is sent) but I personally wouldn't recommend it as mine was lost in the post.
2. For journeys between Germany and most other European countries, Railplus (25%) discount applies on the non-German section for holders of BahnCards and the normal BahnCard discount applies for the rest of the journey.
CD (Czech Railways) have their own special rate for international journeys and a special international rate sold by foreign companies such as DB, the latter of which is 2/3 times higher than the domestic rate. It would therefore be significantly cheaper for you to buy a ticket from the domestic ticket counter in Prague for the trip to the border and buy a ticket from a station in Germany (or on an EC from the DB guard for a small supplement of 10% or in this case the minimum of 2€) from the border to Dresden with the 50% BahnCard discount.
For Czech fares see
http://jizdenka.idos.cz/. Praha hl. n. - Schöna (Gr) costs 192Kc (7.62€) (275Kc CD international rate), Schöna (Gr) - Dresden seems to cost around 5/6 € with BahnCard 50 discount (10/12€ full fare). So you would save around 6/7€ by splitting the journey (factoring in the on-board supplement and assuming you buy a BahnCard 50 - otherwise the saving by splitting would be greater).
The through DB fare costs 32.60€ /21.60€ with BahnCard 50 (local trains) or 33.70€/22.15€ with BahnCard 50 (EC - only relevant in Germany I believe).
The maths suggests that first fare would logically seem to be made up of c. 11€40 / 5€70 (50% BahnCard discount) Dresden - Schöna (Gr) and 21€60 / 16€20 (25% Railplus discount) Schöna (Gr) - Prague, suggesting that the DB international rate is 21€60. The difference between the two fares is 1.10€ without the BahnCard 50 and 0.55€ with the BahnCard 50, suggesting that the difference in fares applies in Germany and that this is the difference between the regional (category C) fare and the IC/EC (category B) fare in Germany. The Czech Railways also seem to have an international rate for Schöna (Gr) - Dresden at 14€. There are lots of threads about this at
Drehscheibe (in German) - if you know what you are doing on this route there are savings to be had. This thread is specifically about the journey you want to make:
http://www.drehscheibe-foren.de/foren/read.php?30,5308146
3. The direction in which you do the journey is irrelevant in terms of the fares but it may affect which tickets you can practically buy.
