I think you can forget the workflow / work items / workflow logs etc. The problem is purely in the background report RPTARQPOST. The report cannot post the request data into the infotype. Why? Have a talk with a time management specialist - he/she can probably present you lots of ideas why a leave request cannot be posted to the infotype 2001. (Or you could try to manually enter the leave request data to the infotype in PA30, and see what is the possible error.)
It is possible that you will never find a reason for the issues number 1. For the second issue: Execute the report RPTARQPOST in SE38. Set the flag into the "Display log" checkbox. As far as I remember this will then display a log of the posting run, and possibly show you the error message(s). Or if this "Display log" checkbox has been set up for the variant that is used for the background job, you might be able to find the log in SM37.
Regards,
Karri