The SharePoint Business Data List Connector is used to simply connect a SharePoint list with external LOB data, e.g. from databases, CRM or ERP systems.

Yes, you can add additional fields after list creation without any restrictions. You can map this newly added columns to fields in your select statement using simple naming conventions. If the columns are not found in the select statement's result set, they remain untouched while updating.
In this way you can add manually edited information to your list.
You can add columns of special type too, e.g. calculated columns or lookups.

Fig.: You can edit BDLC list items as usual in custom Sharepoint lists using the title column.
To allow editing of BDLC list items usually a title column is used. To have a title column in your SQL result set available, please use a select statement like this:
"Select MyID as Title, Description, MyOtherColumns from MyTableOrView"
After the structure is created and the data is updated you can modify the view to render a link to detail view or edit menu in the title column in the view settings:

Fig.: Modify the view settings for rendering the title column to allow a link to detail view or edit menu.
By default in the SharePoint BDLC list the title column is used in view - without any additional link or menu. You can modify this in the view settings dialog. Please choose Title (linked to item) or Title (linked to item with edit menu) insted of Title to display the links in your view as required.