C# - More Efficient Database Access?

I am new to databases and linq, so my problem may be considered trivial. I currently start all my db requests in each class with:

DataClassesDataContext db = new DataClassesDataContext()


Then I proceed to make whatever linq request I need within the method and carry on with the main application logic.

Now, two interesting queries:

1) I believe I have seen people wrapping db usage within 'using'. Such as:

using (DataClassesDataContext db = new DataClassesDataContext())
{
...
}

If this is correct, then doesn't it mean that my class can't use a member 'db' variable anymore, but rather those db requests need to be made within each function call? Also, what exactly would happen if I don't use 'using' within the calls?

2) Running my app with SQL Profiler enabled, I see lots of connections opening and closing. Does this means that each

DataClassesDataContext call makes a separate connection? It seems inefficient, so is the right way to actually make the DataClassesDataContext object a static within each class being used?