A number of ppl do sleep on the beach.. but not for more than a cpl of nights..

You really don't want the dogs for company beyond a point..The hippies around Anjuna mostly shack up in small guesthouses/budget hotels located around Anjuna..
If you're staying 3 weeks, Taj Holiday Village is located in a good place to cash in on the action at Calangute/Baga beaches..There is also a new property located close to Taj, called "The O Hotel". Anjuna is merely a 15mins drive away..
Closer to Anjuna, there is a Country Inn property..which is suitable for long-stays.. It has self-catering serviced apartments plus normal rooms as well.