A Childish Problem

Bengt has no children of his own, for various reasons. Mainly because he's such a big baby himself, most likely. He does occasionally enjoy the company of children, though. Particularly the geeks. From them, he has now learned a classic old problem. The task is to continue the sequence:
1
11
21
1112
3112
211213

1. What is the next element in the sequence? It's probably easier if you think like a child.
   
2. We can imagine three possibilities for the long term behaviour of the sequence: either it settles on one element, repeating that, or it goes into a loop, repeating a subsequence, or it continues forever without looping. Which one is it?
   
3. We could start the sequence with some other start value. Which of the three behaviours are possible?