A) As per second proviso to Section 25(1) any SEZ unit must take a separate registration as distinct from the place of business located outside SEZ. Further any supplies to and from SEZ will only suffer IGST (not CGST/SGST). Therefore the question of transfer of CGST and SGST to an SEZ unit can never arise.
B) This query needs further elaboration. Please note that you can ask your DTA suppliers to issue zero-rated invoice to SEZ unit as provided in Section 16(1)(b) of IGST Act by uploading LUT in their GST portal account in Form GST-RFD-11. FYKI, Customs do not levy IGST for imports slated for supply to SEZ units. The only caveat is - the supplies have to be for authorised operations. SEZ authorities have issued in 2018 a list of authorised services - you may go through the same. Thus I do not foresee a situation wherein you will need to pay IGST on your export/ SEZ supplies and then claim refund as the paramount objective I presume of this query is to set off the ITC with the IGST payable on exports. Is it not?
Further please note as supplies to DTA from SEZ will be processed through Customs there is no way you will be able to set off the ITC with the GST payable on DTA sales.
Further-more, as all exports from SEZ go through SEZ online portal and not ICEGATE portal I contemplate (EXPERTS - please correct) the facility of exporting from SEZ with payment of IGST is at present not available.
Also, hectic parleys were underway, a few months back, to link SEZ online with ICEGATE portal (rechristened as ICEGATE-2). As on date the same is yet to fructify.