Is there any general rule on SQL query complexity Vs performance?

Question

1)Are SQL query execution times O(n) compared to the number of joins, if indexes are not used? If not, what kind of relationship are we likely to expect? And can indexing im

Answer 1

Check out how clustered vs non-clustered indexes work

That is from a pure technical point of view...for an easy explanation my good buddy mladen has written a simple article to understand indexing.

Indexes definately help but I do recommend the reads to understand the pros and cons.