Yes the posters can't really be read (although they're not aimed at us!) from the main station platforms but you can definitely see them from nearby platforms or by walking up onto the footbridge nearby that leads to the railway park next door - its quite an interesting place to wander around if you have a spare half hour.
I recall going to catch a particularly early (ca. 06:00) service to Kaunas and seeing a rake of RZD carriages. Notably all of the customs and border equipment is still there and turned on and you can see it when you walk through the subway under the platforms. Remember also that photography isn't technically allowed inside of station buildings, and there are signs to this effect. You see similar ones in shops, malls etc so it isn't personal to rail enthusiasts. Nobody has ever stopped me photographing the trains themselves though.
The service does indeed involve changing at Mockava and its pretty efficiently done. Just remember that your seat reservation applies to both services - so sit in the same carriage number and seat on each train. The Lithuanian part of the journey can and does get fully booked as its only a two-car set.
Previously trains did run to Kaunas (at one point from Warsaw etc, then it became a weekend-only service from Białystok before this current iteration).
As for Kraków, it doesn't have a huge rail network, though the local rail operator (Koleje Małopolskie) does run a couple of branches off the mainlines. One goes to Wieliczka Rynek-Kopalnia, which is a short walk from the famous salt mine, and the other goes to the Airport. The fares are pretty inexpensive by British standards. It does have a huge tram network though, and you'll still find some old Konstal trams knocking about. It seemed to be line 52 on weekdays (before about 19:00-20:00) and line 6 on weekends. You can buy 24hr tickets and the like on the Jakdojade app which works for most Polish cities.
