SQL Server 2012 Job History Missing
While this only addresses a small part of your question (and you may already be aware):

When you right-click on a job and choose "Start Job at step...", the window that opens does not close automatically when the job is finished. You have to manually close the window (which can be done before or after the job completes).

Once the "Execute job" line in the window has a status (whether success or error), there should (normally) be an entry in sysjobhistory, even if the window hasn't closed (just confirmed in my system).