Hello Assen,
to 1) If the mapping of document types is ok, (Customizing the ECC and GTS) it would be enough to trigger the tansfer
to 2) you can try the SAP standardprogram RV60SBAT.
But take a look at Dave answer to Diwakar Reddy probelm Proforma Invoice to GTS
Hope this helps a bit
Regards,
Thomas