Strange behaviour with Computed Columns in SQL-Server
2.Because nothing is stored for the computed column, I assume no
  index can be created for the column.


This assumption is not true - either kind can be indexed. The computed column must be deterministic in either case but when the computed column is persisted, the requirement that the computation is also precise is relaxed (ie it can involve floating point operations).


  How can an index be created for something that is not persisted and is
  this detrimental in the long run?


The result of the function is 'persisted' in the index in either case - the only difference is whether it is persisted in the table.