On my last visit to Amsterdam, I did not buy any ticket for the tram. I just entered the tram, asked the tram driver how much the fare was to the destination, and paid the fare directly ( there is a small box where you can put the coins) and just alight at the destination. The price would be around 2.60 Euro for 1 hour trip. Means if you ride the tram 2 times within 1 hour, you don't need to pay for the second ride, as long as you can show the ticket as the proof.
For your question regarding tickets that last more than 3 days, there is 24-, 48-, 72-, 96-, 120-, 144- and 168- hour anonymous OV-chipcards. So your best bet should be 72 hours OV-Card. You can buy this tickets all big supermarkets, post office and of course, the central station.
The tram starts working from 06.00 until 00.30 the next morning.
Note that Amsterdam is not a very big city, you can just walk from Van Gogh Museum (South Amsterdam) to Central Station (North Amsterdam) within approximately 1 hour.
Please read this article for more information.