1

Normally (usually) everybody buy the tickets 1 or 2 days before at the bus station itself. Another option is "to show up at the busstation the day itself" but slightly earlier (40-50 min) in order you could buy a ticket at the ticket office. Tickets always can be obtained from the driver too. But passengers who already have their tickets board the bus first, others wait aside. That applies for Vilnius and Klaipėda (and some other towns, for example such like Šventoji, Rokiškis etc).
That option won't work in case you go Vilnius -> seaside during high season, it's better to buy the ticket at least 1 week before. Unless the weather is bad, but this is impossible to predict in advance.
As for Druskininkai-Vilnius i personally would never buy in advance because i don't live in Druskininkai, thus i can't know for sure when i decide to leave Druskininkai, so how can i buy the ticket in advance? There are dozens of buses per day leaving for Vilnius, which one will be convenient at the moment that one will be taken ;) .

2

Well, I was there in july and I think to book the tickets before is the best decision :)