Tickets will be very cheap, there's no need for Interrail. Warsaw - Vilnius costs 115 PLN (26€) for example.

The new Vilnius - Riga train should start soon but before that it's best to cross the border by bus.

No, the Bahncard doesn't give you anything.

Hallo

Danke für die schnelle Antwort. 

Weiß wer wo man in Polen, Litauen und Lettland die Bahnticket kaufen kann?

Gruß 

Here you go :

Estonia : https://elron.ee/en

Latvia : https://www.pv.lv/en/

Lithuania : https://ltglink.lt/en

The websites might not always work. Simply buy at the counter.

Some good information from Seat61:

Poland-Lithuania https://www.seat61.com/trains-and-routes/warsaw-to-vilnius-by-train.htm

Lithuania-Latvia  https://www.seat61.com/trains-and-routes/vilnius-to-riga-by-train.htm

Unfortunately there’s not much information on the new direct train Vilnius-Riga starting 27 December. I took the bus on this route and it was 4.5 hours. Check omio.com for times.