I am absolutely new in databases and SQL queries.
Q1. What are the common problems one generally face in database queries? Probably extremely large queries, performance issues, timeout and connectivity errors, import export and restoration errors
Q2. What approach and tools one should be aware of while debugging a SQL query performance?
It will be great if you can share some of the problems faced and how did you went forward for resolving it.
Try to use EXPLAIN before your queries, that will give you a great overview of what's going on under the hood.
Also see: SQL Performance Tips