Yes true. You had to have a 4-D classification
I don't know. Every male 18+ had to register for the draft but not everyone was drafted until they hit the lottery. So, someone with with a 1A or was it 4 A classification could be accepted and work at Bethel, but should they be drafted, because they were in fact a minister serving at Bethel, got the 4D, but since that 4D was based upon their being in Bethel to begin with, leaving could invoke being drafted, I suppose, unless as you say, they continued full time service by pioneering.
I know WT did not want JW to use Bethel as a defense if they were being drafted before going to Bethel.