Point wise answers to your queries are as under:
You need not to transfer your PF from B to C and then C to D. Yo can transfer your PF at B & C to D with separate transfer request.
This question may not arise in light of my answer at Sr. 1 above. But, one should not forget that it the the duty of current employer to initiate the PF transfer, if any, on employee joining, in reasonable time limit. In case employees leaves the service before initiating the PF transfer, the employer normally do not initiate the transfer.
Transfer between exempted and unexempted establishment are effected through Form 13 only. However, I do not know whether this transfer between exempted and unexempted establishment is done online or not. It came to my reading years back that EPFO will provide Annexure-K online to Private PF trusts.
So Mr.SD need to transfer his PF from B to C and then C to D