Can I use Unity to create an app to do the following with touch or mouse: 1. Start with a toolbox of objects that the user can drag to connect them to each other on particular surfaces? 2. Let the user modify a line or rectangle, for example, by dragging part of the line to bend the line or deform (stretch to add shape to) the line?
The answer to your question as stated is, 'yes'.
yes you can do it but there is not any built in functionallity for that. you should build it from the ground up yourself.