Hi Piyush,
Unfortunately, not all dates are captured in a way that can be queried. For example, you can query things like Closed Date or Opened Date, but not the date that a defect was changed to the Fixed state. Essentially it has to be a field available for that item in order to be able to query it. A query using the date the defect was moved to the closed state could look like (ClosedDate >= today-7)
Also when you write a query you have to separate the operators so if your query has two operators it would be like ((Project.Name = "Blue Team") AND (Owner.UserName = "tom@acme.com")). You can add as many conditions as you need, but it does require you to adjust the parentheses. The Parentheses rules may be different than what you expect. For each condition that you add, you need to put a new ( at the beginning, and each condition after the first must end with )). For example:
((((Project.Name = "Blue Team") AND (Owner.UserName = "tom@acme.com")) AND (Iteration.Name = "October Phase One")) AND (Tags.Name = "Critical"))