Yes, you can add more fields to the tasks list very easily. In your task list, go to Settings in the toolbar and click Create Column. You can also go to the List Settings if you like to view all of the settings and add more columns that way to.
When you choose Create Column, you can enter the name for the column (such as 'Location') and the type of data you want to capture.
If you want to add sub tasks, you can add a 'subtask' column, make it a 'lookup' type and point it at the tasks list.
You can add folders too if you like, you could have one folder for each team. Or you can add more task lists, so that you have a separate task list for each team. But those are not always the best options.
One better option is to create a separate team site for each team, this way they have their own task list, and their own document libraries and calendars etc.
If you want all the tasks in one list, another option is to add a column for 'Team' or something like that.
