Temporary tables in stored procedures

Nope. Independent instances of the temporary table will be created per each connection.

Maybe.

Temporary tables prefixed with one # (#example) are kept on a per session basis. So if your code calls the stored procedure again while another call is running (for example background threads) then the create call will fail because it's already there.

If you're really worried use a table variable instead

DECLARE @MyTempTable TABLE 
(
   someField int,
   someFieldMore nvarchar(50)
)

This will be specific to the "instance" of that stored procedure call.

Not really and I am talking about SQL Server. The temp table (with single #) exists and is visible within the scope it is created (scope-bound). Each time you call your stored procedure it creates a new scope and therefore that temp table exists only in that scope. I believe the temp tables are also visible to stored procedures and udfs that're called within that scope as well. If you however use double pound (##) then they become global within your session and therefore visible to other executing processes as part of the session that the temp table is created in and you will have to think if the possibility of temp table being accessed concurrently is desirable or not.