Adding different types of tasks

Hi,

I want to achieve the functionality such that,

When i click 'Add task' button, it opens a popup where task detail is filled and the 'Task type' is filled.

There could be 3 task types T1, T2, T3. The relation between these are T1>T2>T3

i.e

1- T1 cannot be a child of T3 or T2

2- T3 cannot be a direct child of T1 etc.

I want to prevent Task drop if above conditions not satisfied.

Is there any event available which gets called when tasks are re-arranged (drag drop) something like 'ondrop' having info of droped task data and position where it is droped?

also please suggest how to open popup when 'Add'