Issue 1: You don't need to add the Toolbox controls manually. They are added to the appropriate places automatically after you install Telerik Reporting and run Visual Studio. Note that not all of the controls should be available, depending on the currently opened item in VS. For example, only the WebForms Report Viewer is available when you are inside a Web Form. The report items (Table, TextBox, Crosstab, Graph, etc.) are available only when a report is opened in the Report Designer. Thus, the described behavior by you seems to be correct.
Issue 2: I feel this issue is not related to Reporting, but you should consider checking the connection strings which are stored in the report or in the Class Library where the report is located. You should copy these connection string in your application configuration file and make sure they are correct. Otherwise, the report will not be able to connect to the data base. More information on the providers can be found in the SqlDataSource Component