1 You will probably need EPDM 2013 SP3 (ToBeReleased) to run AutoCAD 2013 with the add in.
2 I am not 100% sure, but AutoCAD LT can not run any add in or do any API task (out off the box).
3 You can run a script via the EPDM task, so probably yes. But only if you know AutoCAD API, there is no default task for this like for the SolidWorks plot taks.
1. You need to consult with the "Multi CAD Matrix" to see which annual sp releases of EPDM support which versions of AutoCAD.
2. No: the EPDM Add-Ins only work with full versions.
3. The EPDM Tasks only work for SolidWorks files,.