1) Our default Connection Routing tries to route the connections in order to minimize the number of crossings between shapes and connections. But it might be too slow in many scenarios. We highly suggest you to implement your own Custom Routing Algorithm for this specific scenario.
Please check out this help article for more info:
Diagram Features Routing: Section Default Routing and Section Custom Routing.
2) There is no property to control the appearance of the leaf-nodes in the Layout Settings of the diagram. However, we are not very sure what you are trying to achieve. Is it possible for you to send us some snapshots of the desired effect?
3) You are able to create multiple links which connect 2 particular shapes. However, in order to distinguish them, you have to set different SourceConnectorPosition and TargetConnectorPosition of these connections. Still , if you need to use equal Source and target ConnectorPositions for all connections, you have to use CustomRouting to separate them - the get route points must return different Point collections for every connection. Please check again the Custom Routing Section in the mentioned article - it might be very useful in this scenario.
Let us know if you need further assistance.
All the best,
the Telerik team