Trip from Estonia -> Latvia -> Lithuania -> Poland

Hi all!

This summer I'm planning to travel from Estonia (Tallinn) to Latvia (Riga) to Lithuania (Vilnius) and eventually to Poland (Bialystok/Warszawa). I am entering Tallinn from Stockholm with a boat. Since Eurail doens't support the railway sites for the Baltic states I went to the sites of these countries by myself. My understandings are that it is possible to go from Tallinn to Riga (via Valga), but when I am looking to see if its possible to go from Riga to Vilnius it seems to be trouble. This is mainly because the railway site of Lithuania doesn't seem to be working for me.

It was my plan to go from Riga to Daugavpils, to switch trains en travel further to Vilnius. 

From Vilnius I wanted to go to Kaunas, to go to Bialystok and eventually travel to Warszawa. 

Here on the forum I am reading that travel from Estonia to Latvia isn't possible, however the railway sites of these countries (Elron and Pasazieru Vilciens) say that it is still possible. Via the route I mentioned above. I am wondering if this is true?

Also, does anyone know if its still possible to go from Daugavpils to Vilnius and to go from Vilnius to Bialystok/Warszawa. I am aware that there is a train in the weekend, which is when I am the city. But the site of Lithuanias railway isn't working for me so I can't see when the train is leaving etc. Does someone know more about this?

I am open to all the answers!